PBW bases for $\imath$quantum groups
Representation Theory
2024-07-19 v1 Quantum Algebra
Abstract
We establish PBW type bases for quantum groups of arbitrary finite type, using the relative braid group symmetries. Explicit formulas for root vectors are provided for quantum groups of each rank 1 type. We show that our PBW type bases give rise to integral bases for the modified quantum 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