A categorical approach to dynamical quantum groups. (2nd September 2022)

• Record Type: Journal Article
• Authors: Kalmykov, Artem; Safronov, Pavel
• Is Part Of: Forum of mathematics. Volume 10(2022)
• Publication Date: 2022-09-02
• Subjects: 17B37 -- 16T05 -- 18M15 -- 17B10; Mathematics -- Periodicals; 510
• DOI: 10.1017/fms.2022.68
• Languages: English
• ISSNs: 2050-5094

Abstract

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.