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.

arXiv comment53 pages, minor edits, to appear in Selecta Math

References in corpus (6)

• Quantum symmetric Kac-Moody pairs
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• Canonical bases for tensor products and super Kazhdan-Lusztig theory
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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