The representation theory of groups is a part of mathematics which examines how groups act on given structures. Here the focus is in particular on operations...

mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space...

information about the representation in a more condensed form. Georg Frobenius initially developed representation theory of finite groups entirely based on...

include groups, associative algebras and Lie algebras. The most prominent of these (and historically the first) is the representation theory of groups, in...

In mathematics, the representation theory of the symmetric group is a particular case of the representation theory of finite groups, for which a concrete...

Modular representation theory is a branch of mathematics, and is the part of representation theory that studies linear representations of finite groups over...

complete classification of finite simple groups. Group theory has three main historical sources: number theory, the theory of algebraic equations, and...

aspects of the theory of finite groups in great depth, especially the local theory of finite groups and the theory of solvable and nilpotent groups. As a...

of a group. There is a direct relationship between the Fourier transform on finite groups and the representation theory of finite groups. The set of complex-valued...

worked on representation theory of finite groups), Richard Brauer's modular representation theory and Issai Schur's papers. The theory of Lie groups, and more...

specifically in group theory, the phrase group of Lie type usually refers to finite groups that are closely related to the group of rational points of a reductive...

product of linear maps. One can extend the notion of tensor products to any finite number of representations. If V is a linear representation of a group G,...

In the mathematical field of representation theory, a weight of an algebra A over a field F is an algebra homomorphism from A to F, or equivalently, a...

mathematics, the representation theory of the Poincaré group is an example of the representation theory of a Lie group that is neither a compact group nor a semisimple...

permutation representation of a (typically finite) group G {\displaystyle G} can refer to either of two closely related notions: a representation of G {\displaystyle...

classification of finite simple groups (popularly called the enormous theorem) is a result of group theory stating that every finite simple group is either...

in representation theory of groups and algebras. In the group case it says that if M and N are two finite-dimensional irreducible representations of a...

object of representation theory. Salient parts of the theory include: Representation theory of finite groups; Representation theory of Lie groups and more...

the general framework of the representation theory of semisimple Lie algebras. The finite-dimensional representations of the connected component SO (...

For such groups, a typical goal of representation theory is to classify all finite-dimensional irreducible representations of the given group, up to isomorphism...

automorphism groups, and their representation theory. For the remainder of this article, "symmetric group" will mean a symmetric group on a finite set. The...

irreducible representation of the group of invertible linear transformations G L ( V ) {\displaystyle GL(V)} . All irreducible representations of G L ( V...

Austrian-born American mathematician who worked in finite group theory and representation theory. His contributions provided elementary infrastructure...

Embodied agent Game character (disambiguation) Representation theory of finite groups § Representation ring Virtual actor Virtual agent (disambiguation)...

theorem (finite groups) Lagrange's theorem (group theory) Lie–Kolchin theorem (algebraic groups, representation theory) Maschke's theorem (group representations)...

In group theory, the induced representation is a representation of a group, G, which is constructed using a known representation of a subgroup H. Given...

Heinrich Maschke, is a theorem in group representation theory that concerns the decomposition of representations of a finite group into irreducible pieces. Maschke's...

inventor of the representation theory of finite groups. The theorem was originally stated in terms of character theory. Let G be a finite group with a subgroup...

modular representation theory of finite groups relating the degrees of the complex irreducible characters in a Brauer block and the structure of its defect...

all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced...