representation theory

== English == === Noun === representation theory (countable and uncountable, plural representation theories) (mathematics, algebra) A branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. 1989 [Clarendon Press], Robert J. Baston, Michael G. Eastwood, The Penrose Transform: Its Interaction with Representation Theory, 2016 Dover edition. 2005, Andrea Brini, Francesco Regonati, Antonio Teolis, Combinatorics and Representation Theory of Lie Superalgebras over Letterplace Superalgebras, Hongbo Li, Peter J. Olver, Gerald Sommer (editors), Computer Algebra and Geometric Algebra with Applications: 6th International Workshop IWWM and International Workshop GIAE, Springer, LNCS 3519, page 239, As an application, we describe in detail the way to specialize general results to the representation theory of the symmetric group and to classical invariant theory. ==== Usage notes ==== Almost always used in the singular, but often qualified by the category of structure represented. === See also === category theory