Serre-Lusztig relations for $ı$quantum groups III

Abstract

let ${\tilde{\mathbf{U}}}^{ı}$ be a quasi-split universal $ı$quantum group associated to a quantum symmetric pair $(\tilde{\mathbf{U}},{\tilde{\mathbf{U}}}^{ı})$ of Kac-Moody type with a diagram involution $\tau$. We establish the Serre-Lusztig relations for ${\tilde{\mathbf{U}}}^{ı}$ associated to a simple root $i$ such that $i\ne \tau i$, complementary to the Serre-Lusztig relations associated to $i=\tau i$ which we obtained earlier. A conjecture on braid group symmetries on ${\tilde{\mathbf{U}}}^{ı}$ associated to $i$ disjoint from $\tau i$ is formulated.

13 pages, accepted for publication

Cited by in corpus (1)

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