A categorical approach to dynamical quantum groups

Artem Kalmykov, Pavel Safronov
2022 Forum of Mathematics, Sigma  
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
more » ... tural Weyl symmetry of the parabolic restriction functor using Zhelobenko operators and show that it gives rise to the action of the dynamical Weyl group.
doi:10.1017/fms.2022.68 fatcat:o7zbr24sibearcopqsbhcv5asu