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

Abstract

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

53 pages, minor edits, to appear in Selecta Math

References in corpus (1)

• Serre-Lusztig relations for $ı$quantum groups III

Cited by in corpus (2)

• A Drinfeld type presentation of affine $ı$quantum groups II: split BCFG type
• A Drinfeld type presentation of affine $ı$quantum groups I: split ADE type