English

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 ı\imathquantum groups of arbitrary finite types have been constructed by Wang and the author. In this paper, we extend that construction to ı\imathquantum groups of Kac-Moody type. We formulate root vectors for ı\imathquantum groups in both recursive forms and closed ı\imathdivided power forms. We show that the relative braid group symmetries send root vectors to root vectors.

Keywords

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