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A categorical approach to dynamical quantum groups

By Artem Kalmykov and Pavel Safronov

Abstract

We present a categorical point of view on dynamical quantum groups in terms of categories of Harish-Chandra bimodules. We prove Tannaka duality theorems for forgetful functors into the monoidal category of Harish-Chandra bimodules in terms of a slight modification of the notion of a bialgebroid. Moreover, we show that the standard dynamical quantum groups $F(G)$ and $F_q(G)$ are related to parabolic restriction functors for classical and quantum Harish-Chandra bimodules. Finally, we exhibit a natural Weyl symmetry of the parabolic restriction functor using Zhelobenko operators and show that it gives rise to the action of the dynamical Weyl group.Comment: 47 pages; corrected coproduct in section 4.

Topics: Mathematics - Representation Theory, Mathematics - Category Theory, Mathematics - Quantum Algebra
Year: 2020
OAI identifier: oai:arXiv.org:2008.09081

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