Peter-Weyl bases, preferred deformations, and Schur-Weyl duality

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 un...

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Bibliographic Details
Main Authors Giaquinto, Anthony, Gilman, Alex, Tingley, Peter
Format Journal Article
LanguageEnglish
Published 14.06.2019
Subjects
Mathematics - Quantum Algebra
Mathematics - Representation Theory
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Summary: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.
DOI:10.48550/arxiv.1906.06284