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

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.