By an ultra classical result, the tensor product of a simple representation of π€π©n(β) 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 1-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 π€π©n(β) + π€π©n(β) 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.
This video is part of the European Non-Associative Algebra Seminar series.
