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

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

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