in a Media arts medium . The degree to which an artistic representation resembles the object it represents ... representation.htm University of Chicago DEFAULTSORT RepresentationArts Category Aesthetics Category ...Representation is the use of signs that stand in for and take the place of something else. ref name Mitchell1995 Mitchell, W. 1995, Representation , in F Lentricchia & T McLaughlin eds , Critical Terms for Literary Study , 2nd edn, University of Chicago Press, Chicago ref It is through representation ... Representation has been associated with aesthetics art and semiotics signs . Mitchell says representation .... 13 The term representation carries a range of meanings and interpretations. In literary theory , representation ..., Media and society an introduction , 3rd edn, Oxford University Press, South Melbourne, 2005 ref Representation .... ref name Stadler2005 Defining representation Image Mona Lisa, by Leonardo da Vinci, from C2RMF retouched.jpg ... re , intensive prefix, praesentare to present, lit. to place before . A representation is a type of recording ... in Hadrian s Villa mosaic Since ancient times representation has played a central role in understanding ... theory who considered literature as simply one form of representation. ref name Childers1995 Childers ..., New York, 1995 ref Aristotle for instance, considered each mode of representation, verbal, visual or musical, as being natural to human beings. ref name Vukcevich2002 Vukcevich, M 2002, Representation ... animals is their ability to create and manipulate signs. ref name Mitchell1990 Mitchell, W, Representation ..., in contrast, looked upon representation with more caution. He recognised that literature is a representation ... Practice , Open University Press, London, 1997. ref For Plato, representation, like contemporary ... things . Plato believed that representation needs therefore, to be controlled and monitored due to the possible ... name Mitchell1995 From childhood man has an instinct for representation, and in this respect man differs ... things. ref name Mitchell1995 p. 11 Aristotle discusses representation in three ways The object ... more details
Wiktionarypar representation represent Representation can refer to Representation politics , one s ability to influence the political process Representative democracy Permanent Representation, a type of diplomatic mission Representation of the International NGO the representative office of the International non governmental organization INGO mission Representationarts , the depiction and ethical concerns of construction in visual arts and literature. Depiction is meaning conveyed through pictures Representation psychology , a hypothetical internal cognitive symbol that represents external reality Representation mathematics and group representation Multiple representations mathematics education Representation chemistry Representation systemics Knowledge representation , the study of formal ways to describe knowledge Legal representation or advocacy is provided by lawyers Lobbying for a group of individuals or companies In unionised workplaces, Union steward shop stewards and union executives can represent employees The legal status of a statement made with regards to Contract contract law A fiction of the law which causes a person to enter into another s right of succession, called Representation succession representation , and also called substitution . Represent can refer to Represent Fat Joe album Represent Fat Joe album , a 1993 album by Fat Joe Represent Compton s Most Wanted album Represent Compton s Most Wanted album , a 2000 album by Compton s Most Wanted Represent , a 1994 album by DJ Magic Mike Represent song Represent song , a song by Nas Represent , a 2009 song by The Red Jumpsuit Apparatus Represent Weezer song Represent , a 2010 single by Weezer released as an unofficial anthem for the United States men s national soccer team See also Reprazent disambig cs Reprezentace de Repr sentation es Representaci n fr Repr sentation homonymie nl Representatie pt Representa o ro Reprezentare ru simple Representation fi Representaatio sv Representation ... more details
The term complex representation has slightly different meanings in mathematics and physics. In mathematics , a complex representation is a group representation of a group or Lie algebra on a complex vector space. In physics , a complex representation is a group representation of a group or Lie algebra on a complex vector space that is neither real representation real nor pseudoreal representation pseudoreal . In other words, the Group mathematics group elements are expressed as complex matrices, and the complex conjugate of a complex representation is a different, non equivalent representation. For compact groups, the Frobenius Schur indicator can be used to tell whether a representation is real, complex, or pseudo real. For example, the N dimensional fundamental representation of SU N for N greater than two is a complex representation whose complex conjugate is often called the antifundamental representation . algebra stub Category Representation theory of groups ... more details
In mathematics , an antifundamental representation is the complex conjugate of the fundamental representation , although the distinction between the fundamental and the antifundamental representation is a matter of convention. However, these two are often non equivalent, because each of them is a complex representation . Category Representation theory of Lie groups geometry stub ... more details
In mathematics and theoretical physics , a bifundamental representation is a representation theory representation obtained as a tensor product of two fundamental representation fundamental or antifundamental representation antifundamental representations. For example, the MN dimensional representation M , N of the group math SU M times SU N math is a bifundamental representation. These representations occur in quiver diagram s. algebra stub Category Abstract algebra ... more details
The adjoint representation can refer to Ad the adjoint representation of a Lie group G ad the adjoint representation of a Lie algebra math mathfrak g math , see adjoint endomorphism . mathdab ... more details
In mathematics , a linear representation &rho of a group G is a monomial representation if there is a finite index subgroup H and a one dimensional linear representation &sigma of H , such that &rho is equivalent to the induced representation Ind sub H sub sup G sup &sigma . Alternatively, one may define it as a representation whose image is in the monomial matrices . Here for example G and H may be finite group s, so that induced representation has a classical sense. The monomial representation is only a little more complicated than the permutation representation of G on the coset s of H . It is necessary only to keep track of scalars coming from &sigma applied to elements of H . References Springer id m m064780 title Monomial representation Category Representation theory of groups Algebra stub it Rappresentazione monomiale ... more details
Unreferenced date December 2009 Orphan date December 2009 This article addresses the notion of quasiregularity in the context of representation theory and topological algebra . For other notions of quasiregularity in mathematics , see the disambiguation page quasiregular . In mathematics , quasiregular representation is a concept of representation theory , for a locally compact group G and a homogeneous space G H where H is a closed subgroup . In line with the concepts of regular representation and induced representation , G acts on functions on G H . If however Haar measure s give rise only to a quasi invariant measure on G H , certain correction factors have to be made to the action on functions, for L sup 2 sup G H to afford a unitary representation of G on square integrable function s. With appropriate scaling factors, therefore, introduced into the action of G , this is the quasiregular representation or modified induced representation. DEFAULTSORT Quasiregular Representation Category Unitary representation theory Category Topological groups ... more details
In mathematics , if G is a group mathematics group and &rho is a linear representation of it on the vector space V , then the dual representation Overline &rho is defined over the dual vector space Overline V as follows ref Lecture 1 of Fulton Harris ref Overline &rho g is the transpose of a linear map transpose of &rho g sup &minus 1 sup for all g in G . Then Overline &rho is also a representation, as may be checked explicitly. The dual representation is also known as the contragredient representation . If math mathfrak g math is a Lie algebra and &rho is a representation of it over the vector space V , then the dual representation Overline &rho is defined over the dual vector space Overline V as follows ref Lecture 8 of Fulton Harris ref Overline &rho u is the transpose of &minus &rho u for all u in math mathfrak g math . Overline &rho is also a representation, as can be explicitly checked. For a unitary representation , the conjugate representation and the dual representation coincide, up to equivalence of representations. Generalization A general ring Module mathematics module does not admit a dual representation. Modules of Hopf algebra s do, however. See also Complex conjugate representation Kirillov Character Formula References references Category Representation theory of groups fr Repr sentation duale ... more details
In the mathematics mathematical field of representation theory , a trivial representation is a group representationrepresentation V , &phi of a Group mathematics group G on which all elements of G act as the identity mapping of V . A trivial Representation mathematics representation of an associative algebra associative or Lie algebra is a Lie algebra representation Lie algebra representation for which all elements of the algebra act as the zero endomorphism which sends every element of V to the zero vector. For any group or Lie algebra, an irreducible representation irreducible trivial representation always exists over any field, and is one dimensional, hence unique up to isomorphism. The same is true for associative algebras unless one restricts attention to unital algebra s and unital representations. Although the trivial representation is constructed in such a way as to make its properties seem tautologous, it is a fundamental object of the theory. A subrepresentation is equivalent to a trivial representation, for example, if it consists of invariant vectors so that searching for such subrepresentations is the whole topic of invariant theory . The trivial character is the character mathematics character that takes the value of one for all group elements. References Fulton Harris . Category Representation theory algebra stub zh ... more details
Symbolic representation may refer to Symbolism disambiguation Symbolic linguistic representation In politics, it has to do with a representative in congress or in a group that is seen as being there to represent a group of minorities whether it be gender or cultural groups. See also Symbolic disambiguation Representation disambiguation disambig ... more details
In mathematics , in the representation theory of algebraic group s, a linear representation of an algebraic group is said to be rational if, viewed as a map from the group to the general linear group, it is a rational map of algebraic varieties. Finite direct sums and products of rational representations are rational. A rational math G math module is a module that can be expressed as a sum not necessarily direct of rational representations. see Group representation References http www.jstor.org view 00029327 di994362 99p00143 Extensions of Representations of Algebraic Linear Groups http www.encyclopediaofmath.org index.php Rational representation Springer Online Reference Works Rational Representation Category Representation theory of algebraic groups algebra stub ... more details
In mathematics , especially in the area of abstract algebra known as representation theory , a faithful representation of a group mathematics group G on a vector space V is a linear representation in which different elements g of G are represented by distinct linear mappings g . In more abstract language, this means that the group homomorphism G GL V is injective . Caveat While representations of G over a field K are de facto the same as math K G math modules with math K G math denoting the Group ring Group algebra over a finite group group algebra of the group G , a faithful representation of G is not necessarily a faithful module for the group algebra. In fact each faithful math K G math module is a faithful representation of G , but the converse does not hold. Consider for example the natural representation of the symmetric group S sub n sub in n dimensions by permutation matrices , which is certainly faithful. Here the order of the group is n while the n × n matrices form a vector space of dimension n sup 2 sup . As soon as n is at least 4, dimension counting means that some linear dependence must occur between permutation matrices since 24 16 this relation means that the module for the group algebra is not faithful. Properties A representation V of a finite group G over an algebraically closed field K of characteristic zero is faithful as a representation if and only if every irreducible representation of G occurs as a subrepresentation of S sup n sup V the n th symmetric power of the representation V for a sufficiently high n . Also, V is faithful as a representation if and only if every irreducible representation of G occurs as a subrepresentation of math V otimes n underbrace V otimes V otimes cdots otimes V n text times math the n th tensor power of the representation V for a sufficiently high n . References Springer id F f038170 title faithful representation Category Representation theory algebra stub ... more details
In the mathematics mathematical field of representation theory a real representation is usually a group representationrepresentation on a real number real vector space U , but it can also mean a representation on a complex number complex vector space V with an invariant real structure , i.e., an antilinear ... C is a representation on a complex vector space with an antilinear equivariant map given by complex conjugation . Conversely, if V is such a complex representation, then U can be recovered as the fixed ... concretely in terms of matrices, a real representation is one in which the entries of the matrices ... column vectors. A real representation on a complex vector space is isomorphic to its complex conjugate representation , but the converse is not true a representation which is isomorphic to its complex conjugate but which is not real is called a pseudoreal representation . An irreducible pseudoreal representation V is necessarily a quaternionic representation it admits an invariant quaternionic ... real nor quaternionic in general. A representation on a complex vector space can also be isomorphic to the dual representation of its complex conjugate. This happens precisely when the representation ... of the representation and is the Haar measure with G 1. For a finite group, this is given by math ... is 1, then the representation is real. If the indicator is zero, the representation is complex hermitian , ref Any complex representation V of a compact group has an invariant hermitian form ... form on V . ref and if the indicator is &minus 1, the representation is quaternionic. Examples All representation of the symmetric group symmetric groups are real and in fact rational , since we can ... of copies of the fundamental representation, which is real. Further examples of real representations ... representation . Notes reflist 1 References Fulton Harris . citation first Jean Pierre last Serre ... 6 . Category Representation theory pt Representa o real ... more details
A representation term is a word, or a combination of words, used as part of a data element name . Representation class is sometimes used as a synonym for representation term. In ISO IEC 11179 , a representation class provides a way to Taxonomic classification classify or group data element s. A representation class is effectively a specialized classification scheme . Hence, there is currently some discussion in ISO over the merits of keeping representation class as a separate entity in 11179, versus collapsing it into the general classification scheme facility ref Issue114 . A clear distinction between the two mechanisms, however, is that 11179 allows a data element to be classified by only one representation class, whereas there is no such restriction on other classification schemes. ISO IEC 11179 does not specify that representation terms should be drawn from the values of representation class , though it would make sense to do so, nor does it provide any mechanism to ensure any sort of consistency whatever that might mean between the representation terms used to name a data element, and the representation class used to classify it. The term representation class has been used in metadata ... light on the semantics or meaning of the data element. Definitions of representation class There are several alternate definitions for representation class . Some of these are taken from the ISO documents ... rules. ISO Definitions of representation class From ISO IEC TR 20943 1 First edition 2003 08 01 pdf page 91 B.2.3 Representation class Representation class is the value domain for representation. The set ... element categorized with the representation class amount is different from an element categorized as number ... using them together. Representation class is a mechanism by which the functional and or presentational ... 02 15 3.3.51 data element representation class the class of representation of a data element See also ... to the ISO bugzilla discussion of Representation class External links http standards.iso.org ittf PubliclyAvailableStandards ... more details
Unreferenced stub auto yes date December 2009 Orphan date November 2006 Substantive representation in contrast to descriptive representation is a concept in the legislative branch es of Representation politics representative republic s describing the tendency of representatives to advocate for certain groups. Often, their area of advocacy is in contrast to their background, such as late United States U.S. United States Senate Senator Ted Kennedy Edward Kennedy s advocacy for the poor Kennedy was a scion of one of the richest families in Massachusetts . Constituents vote for representatives by looking at policy stances and past efforts as a representative. DEFAULTSORT Substantive Representation Category Political terms Poli term stub ... more details
In mathematical finite group theory, the vertex of a representation of a finite group is a subgroup associated to it, that has a special representation called a source . Vertices and sources were introduced by harvs txt last Green year 1959 References Citation last1 Green first1 J. A. title On the indecomposable representations of a finite group doi 10.1007 BF01558601 mr 0131454 year 59 month 1958 journal Mathematische Zeitschrift issn 0025 5874 volume 70 pages 430 445 Category Representation theory Category Finite groups ... more details
, Stanislavskian theatre, in which actors experience their roles, remains Representationarts ... by an outside perspective on the role in the art of representation approach to acting. In When Acting ... acting , art of representation , and his own experiencing the role . One symptom of the recurrent ... his own approach of experiencing the role and that of the art of representation . In Stanislavski ... itself 1936, 40 41 . ref In contrast, the approach that Stanislavski calls the art of representation ... artisto rol . ref See Benedetti 1998, 9 11 and Carnicke 1998, 170 . ref In the art of representation ... w Lure w Method of Physical Actions list5 Motivation w The Questions w Relaxation w Art of representationRepresentation list6 Sense Memory w Subtext w Task w Super Task w Through Action w Turning Point ... more details
In representation theory of Lie group s and Lie algebra s, a fundamental representation is an irreducible finite dimensional representation of a semisimple Lie algebra semisimple Lie group or Lie algebra whose highest weight is a fundamental weight . For example, the defining module of a classical Lie group is a fundamental representation. Any finite dimensional irreducible representation of a semisimple Lie group or Lie algebra can be constructed from the fundamental representations by a procedure due to lie Cartan . Thus in a certain sense, the fundamental representations are the elementary building blocks for arbitrary finite dimensional representations. Examples In the case of the general linear group , all fundamental representations are exterior power s of the defining module. In the case of the special unitary group SU n SU n , the n &minus 1 fundamental representations are the wedge products math operatorname Alt k mathbb C n math consisting of the alternating tensor s, for k 1, 2, ..., n &minus 1. The spin representation of the twofold cover of an odd orthogonal group , the odd spin group , and the two half spin representations ... that cannot be realized in the space of tensors. The adjoint representation of the simple Lie group of type E8 mathematics E sub 8 sub is a fundamental representation. Explanation The Representation ... group are indexed by their highest weight representation theory weights . These weights are the lattice ... and extract one copy of the irreducible representation corresponding to that dominant weight. Other uses Outside of Lie theory, the term fundamental representation is sometimes loosely used to refer to a smallest dimensional faithful representation, though this is also often called the standard or defining representation a term referring more to the history, rather than having a well defined mathematical meaning . References Fulton Harris Category Lie groups Category Representation theory algebra ... more details
Adaptive representation is an extension by Francis Heylighen ref Heylighen, Francis 1990 . Representation and Change A Metarepresentational Framework for the Foundations of Physical and Cognitive Science . Communication and Cognition, Ghent, Belgium. ref to Kant s epistemology theory of knowledge . According to Kant, perception passes by the filters of the mind who observes the phenomena. In this line, there exists in the human mind invariant and a priori principles of experience. As an example, one may have imprinted in the brain a Dualism philosophy of mind Cartesian representation of space, a notion of time, color separation and others. This may be called static representation . Heylighen has proposed a revision of these Kantian ideas, in which these principles are not supposed to be invariant and necessary A priori and a posteriori philosophy a priori instead alternative principles exist for the organization of experience in adaptive representations. This opens a path for new investigations in the philosophy of mind and human cognition . References reflist External links http pcp.vub.ac.be books Rep&Change.pdf Web edition of Representation and Change 1999 . Epistemology stub Category Epistemology ... more details
In mathematics mathematical field of representation theory , a symplectic representation is a group representationrepresentation of a group mathematics group or a Lie algebra representation Lie algebra on a symplectic vector space V , which preserves the symplectic form . Here is a nondegenerate skew symmetric bilinear form math omega colon V times V to mathbb F math where F is the field mathematics field of scalars. A representation of a group G preserves if math omega g cdot v,g cdot w omega v,w math for all g in G and v , w in V , whereas a representation of a Lie algebra g preserves if math omega xi cdot v,w omega v, xi cdot w 0 math for all in g and v , w in V . Thus a representation of G or g is equivalently a group or Lie algebra homomorphism from G or g to the symplectic group Sp V , or its Lie algebra sp V , If G is a compact group for example, a finite group , and F is the field of complex numbers, then by introducing a compatible unitary structure which exists by an averaging argument , one can show that any complex symplectic representation is a quaternionic representation . Quaternionic representations of finite or compact groups are often called symplectic representations, and may be identified using the Frobenius Schur indicator . References Fulton Harris . Category Representation theory Category Symplectic geometry algebra stub it Rappresentazione simplettica ro Reprezentare simplectic ... more details
In mathematics mathematical field of representation theory , a quaternionic representation is a group representationrepresentation on a complex number complex vector space V with an invariant quaternionic ... the division algebra of quaternion s . From this point of view, quaternionic representation of a group ... quaternion linear transformations of V . In particular, a quaternionic matrix representation of g ... concepts If V is a unitary representation and the quaternionic structure j is a unitary operator, then V admits an invariant complex symplectic form &omega , and hence is a symplectic representation . This always holds if V is a representation of a compact group e.g. a finite group and in this case ..., amongst irreducible representation s, can be picked out by the Frobenius Schur indicator . Quaternionic representations are similar to real representation s in that they are isomorphic to their complex conjugate representation . Here a real representation is taken to be a complex representation with an invariant ... satisfies math j 2 1. , math A representation which is isomorphic to its complex conjugate, but which is not a real representation, is sometimes called a pseudoreal representation . Real and pseudoreal ... algebra R G . Such a representation will be a direct sum of central simple R algebras, which, by the Artin ... a real or pseudoreal representation is a direct sum of irreducible real representations and irreducible .... Examples A common example involves the quaternionic representation of rotation s in three ... multiplication. By restricting this to the unit quaternions, we obtain a quaternionic representation of the spinor group Spin 3 . This representation &rho Spin 3 &rarr GL 1, H also happens to be a unitary quaternionic representation because math rho g dagger rho g mathbf 1 , math for all g in Spin 3 . Another unitary example is the spin representation of Spin 5 . An example of a nonunitary quaternionic representation would be the two dimensional irreducible representation of Spin 5,1 . More generally ... more details
An affine representation of a topological group topological Lie group Lie group G on an affine space A is a continuity topology continuous smooth function smooth group homomorphism from G to the automorphism group of A , the affine group Aff A . Similarly, an affine representation of a Lie algebra g on A is a Lie algebra homomorphism from g to the Lie algebra aff A of the affine group of A . An example is the action of the Euclidean group E n upon the Euclidean space E sup n sup . Since the affine group in dimension n is a matrix group in dimension n 1, an affine representation may be thought of as a particular kind of linear representation . We may ask whether a given affine representation has a fixed point mathematics fixed point in the given affine space A . If it does, we may take that as origin and regard A as a vector space in that case, we actually have a linear representation in dimension n . This reduction depends on a group cohomology question, in general. See also Group action Projective representation References citation first1 Elisabeth last1 Remm first2 Michel last2 Goze title Affine Structures on abelian Lie Groups arxiv math 0105023 journal Linear Algebra and its Applications volume 360 year 2003 pages 215&ndash 230 doi 10.1016 S0024 3795 02 00452 4 . Category Group theory Category Homological algebra Category Representation theory Category Representation theory of Lie algebras Category Representation theory of Lie groups algebra stub eo Afina prezento pt Representa o afim ... more details
Image Schop welt 2ed.jpg right thumb The title page of the expanded 1844 publication The World as Will and Representation ... this title The World as Will and Representation appeared by E.F.J.Payne who also translated several other works of Schopenhauer as late as in 1958 ref Arthur Schopenhauer The world as will and representation ... in 1966 and 1969 . ref Arthur Schopenhauer The world as will and representation , Courier Dover ... form of experience. Schopenhauer saw the human will as our one window to the world behind the representation ... representation and thing in itself could be understood by analogy to the relationship between human will and human body. According to Schopenhauer, the entire world is the representation of a single ... forms as existing on an intermediate ontology ontological level between the representation ... in his career 1814 1818 and culminated in the publication of the first volume of Will and Representation ... . Representation He used the word representation Vorstellung to signify the mental idea or image of any ... . This concept includes the representation of the observing subject s own body. Schopenhauer ... reality behind the representation that provided the matter of perception, but lacked form. Kant ... imposed on the world by the human mind in order to create the representation, and these factors were ... are as follows. Supplements to the First Book First Half The Doctrine of the Representation of Perception ... Second Half The Doctrine of the Abstract Representation or of Thinking V. On the Intellect Devoid ... Remarks on the Aesthetics of the Plastic and Pictorial Arts XXXVII. On the Aesthetics of Poetry ... Wagner were all strongly influenced by his work. For Nietzsche, the reading of The World as Will and Representation ... , Oxford University Press, 1997 reprint , ISBN 0 19 823722 7 Schopenhauer , Arthur. The World as Will and Representation ... in German to The World as Will and Representation 1998 Notes references External links http www.zeno.org ... As Will And Representation Category 1819 books volume 1 Category 1844 books volume 2 Category Philosophy ... more details
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