Braid group actions for quantum symmetric pairs of type AIII/AIV

Abstract

In the present paper we construct braid group actions on quantum symmetric pair coideal subalgebras of type AIII/AIV. This completes the proof of a conjecture by Kolb and Pellegrini in the case where the underlying Lie algebra is ${\mathfrak{sl}}_n$. The braid group actions are defined on the generators of the coideal subalgebras and the defining relations and braid relations are verified by explicit calculations.

Substantial revision following referee comments. Section 2 has been shortened considerably. Lemmas 3.10 to 3.15 have been condensed into a single proof of Theorem 3.8. Sections 3.2 and 3.3 are now Sections 4 and 5, respectively. Removed Propositions 3.22 to 3.26 and replaced with Section 4.2. The Appendix has been split into three parts for readability. To appear in Journal of Algebra;38 pages