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arXiv:2407.13127 [math.RT]AbstractReferencesReviewsResources

PBW bases for $\imath$quantum groups

Ming Lu, Ruiqi Yang, Weinan Zhang

Published 2024-07-18Version 1

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

Comments: 33 pages; comments are welcome
Categories: math.RT, math.QA
Subjects: 17B37
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