English

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

Quantum Algebra 2020-07-21 v2

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 sln\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.

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