Relative braid group symmetries on $\imath$quantum groups of Kac-Moody type
Quantum Algebra
2025-04-08 v3 Representation Theory
Abstract
Recently, relative braid group actions on quantum groups of arbitrary finite types have been constructed by Wang and the author. In this paper, we extend that construction to quantum groups of Kac-Moody type. We formulate root vectors for quantum groups in both recursive forms and closed divided power forms. We show that the relative braid group symmetries send root vectors to root vectors.
Cite
@article{arxiv.2209.12860,
title = {Relative braid group symmetries on $\imath$quantum groups of Kac-Moody type},
author = {Weinan Zhang},
journal= {arXiv preprint arXiv:2209.12860},
year = {2025}
}
Comments
v3, corrected formulas (3.17)-(3.18); 46 pages