A categorical approach to dynamical quantum groups

Artem Kalmykov, Pavel Safronov

Research output: Working paper

Abstract / Description of output

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 Fq(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.
Original languageEnglish
PublisherArXiv
Number of pages47
Publication statusPublished - 24 Aug 2020

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