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.