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...

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

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...

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

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

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 and wrote the first book about group theory in the English language: Theory of Groups of Finite Order),...

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

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...

in terms of the more concrete ones, using homomorphisms, actions and modules. An early pioneer of the representation theory of finite groups was Ferdinand...

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...

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

for the representation theory of the group of diffeomorphisms of a smooth manifold M is the initial observation that (for M connected) that group acts transitively...

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...

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

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...

operated on, the result is also within the group). Compact groups are a natural generalization of finite groups with the discrete topology and have properties...

work in the representation theory of finite groups. Her contributions were honored with the 1990 Noether Lecture. She served as president of the Association...

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...

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

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

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

polynomials. In representation theory they are the characters of polynomial irreducible representations of the general linear groups. The Schur polynomials...