English

PBW bases for $\imath$quantum groups

Representation Theory 2024-07-19 v1 Quantum Algebra

Abstract

We establish PBW type bases for ı\imathquantum groups of arbitrary finite type, using the relative braid group symmetries. Explicit formulas for root vectors are provided for ı\imathquantum groups of each rank 1 type. We show that our PBW type bases give rise to integral bases for the modified ı\imathquantum groups. The leading terms of our bases can be identified with the usual PBW bases in the theory of quantum groups.

Keywords

Cite

@article{arxiv.2407.13127,
  title  = {PBW bases for $\imath$quantum groups},
  author = {Ming Lu and Ruiqi Yang and Weinan Zhang},
  journal= {arXiv preprint arXiv:2407.13127},
  year   = {2024}
}

Comments

33 pages; comments are welcome

R2 v1 2026-06-28T17:45:24.068Z