ﻻ يوجد ملخص باللغة العربية
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.
The $imath$Serre relations and the corresponding Serre-Lusztig relations are formulated for arbitrary $imath$quantum groups arising from quantum symmetric pairs of Kac-Moody type. This generalizes the main results in [CLW18, CLW20].
let $widetilde{bf U}^imath$ be a quasi-split universal $imath$quantum group associated to a quantum symmetric pair $(widetilde{bf U}, widetilde{bf U}^imath)$ of Kac-Moody type with a diagram involution $tau$. We establish the Serre-Lusztig relations
This paper studies classical weight modules over the $imath$quantum group $mathbf{U}^{imath}$ of type AI. We introduce the notion of based $mathbf{U}^{imath}$-modules by generalizing the notion of based modules over the quantum groups. We prove that
We show that the $imath$Hall algebra of the Jordan quiver is a polynomial ring in infinitely many generators and obtain transition relations among several generating sets. We establish a ring isomorphism from this $imath$Hall algebra to the ring of s
$imath$quantum groups are generalizations of quantum groups which appear as coideal subalgebras of quantum groups in the theory of quantum symmetric pairs. In this paper, we define the notion of classical weight modules over an $imath$quantum group,