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 . 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.
Keywords
Cite
@article{arxiv.1909.11215,
title = {Braid group actions for quantum symmetric pairs of type AIII/AIV},
author = {Liam Dobson},
journal= {arXiv preprint arXiv:1909.11215},
year = {2020}
}
Comments
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