Geodesic
A categorical approach to dynamical quantum groups
Forum of Mathematics, Sigma, Tome 10 (2022)

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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. 
@article{10_1017_fms_2022_68,
     author = {Artem Kalmykov and Pavel Safronov},
     title = {A categorical approach to dynamical quantum groups},
     journal = {Forum of Mathematics, Sigma},
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Artem Kalmykov; Pavel Safronov. A categorical approach to dynamical quantum groups. Forum of Mathematics, Sigma, Tome 10 (2022). doi: 10.1017/fms.2022.68

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