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

Abstract: We establish automorphisms with closed formulas on quasi-split

i m a t h

quantum groups of symmetric Kac-Moody type associated to restricted Weyl groups. The proofs are carried out in the framework of

i m a t h

Hall algebras and reflection functors, thanks to the

i m a t h

Hall algebra realization of

i m a t h

quantum groups in our previous work. Several quantum binomial identities arising along the way are established.

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