It turns out that a representation of a Lie algebra g is the same thing as a representation of a certain associative algebra U(g). Thus, as with quivers, we can view the theory of …

Representation theory is the study of groups through the lens of linear algebra, allowing us to observe how a group acts on a vector space while making use of all the standard theorems …

We call a representation (π, V) a complex representation if V is a vector space over the complex numbers. Similarly, we say the representation is a real representation if V is a vector space is …

The basic problem of representation theory is to classify all representations of a given group G up to isomorphisms. Good theory exists for finite groups over C, and for compact topological groups.

representation theory. The mathematical definitions make a lot of sense, but it is hard to get an intuitive understand of it, which is why we will lo haven’t seen

May 20, 2016 · Overview of representations and characters of finite groups. Representations of symmetric groups: Young symmetrizers, Sþecht mod-ules, branching rule, Gelfand-Tzetlin …

We begin with a review of the pertinent facts from the representation theory of Lie groups, taking as our rst example the group GL(n; R), a group whose underlying manifold is neither compact …