Peter-Weyl bases, preferred deformations, and Schur-Weyl duality
Quantum Algebra
2019-06-17 v1 Representation Theory
Abstract
We discuss the deformed function algebra of a simply connected reductive Lie group G over the complex numbers using a basis consisting of matrix elements of finite dimensional representations. This leads to a preferred deformation, meaning one where the structure constants of comultiplication are unchanged. The structure constants of multiplication are controlled by quantum 3j symbols. We then discuss connections earlier work on preferred deformations that involved Schur-Weyl duality.
Cite
@article{arxiv.1906.06284,
title = {Peter-Weyl bases, preferred deformations, and Schur-Weyl duality},
author = {Anthony Giaquinto and Alex Gilman and Peter Tingley},
journal= {arXiv preprint arXiv:1906.06284},
year = {2019}
}
Comments
13 pages