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arXiv · 2107.06023

Braid group symmetries on quasi-split $\imath$quantum groups via $\imath$Hall algebras

Ming Lu·Weiqiang Wang
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Abstract

We establish automorphisms with closed formulas on quasi-split $\imath$quantum groups of symmetric Kac-Moody type associated to restricted Weyl groups. The proofs are carried out in the framework of $\imath$Hall algebras and reflection functors, thanks to the $\imath$Hall algebra realization of $\imath$quantum groups in our previous work. Several quantum binomial identities arising along the way are established.

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Ming Lu, Weiqiang Wang. 2021-07-13. Braid group symmetries on quasi-split $\imath$quantum groups via $\imath$Hall algebras. https://arxiv.org/abs/2107.06023

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