Clebsch-Gordan revisited

Abstract: By an ultra classical result, the tensor product of a simple representation of gl(n,C) and its defining representation decomposes as a direct sum of simple representations without multiplicities. This means that for each highest weight, the space of highest weight vectors is one dimensional. We will give an explicit construction of these highest weight vectors, and show that they arise from the action of certain elements in the enveloping algebra of gl(n,c)+gl(n,C) on the tensor product. These elements are independent of the simple representation we started with, and in fact produce highest weight vectors in several other contexts. (Joint with Joanna Meinel from Bonn University)

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar