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PBW bases for $\imath$quantum groups

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arxiv 2407.13127 v1 pith:JNJNRD76 submitted 2024-07-18 math.RT math.QA

Ming Lu , Ruiqi Yang , Weinan Zhang This is my paper · ORCID
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keywords basesgroupsquantumimathtypearbitrarybraidestablish
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abstract

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.

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  1. Braid group symmetries on Poisson algebras arising from quantum symmetric pairs

    math.QA 2025-07 conditional novelty 7.0 of 10

    For every finite type quantum symmetric pair, the braid group action and a PBW basis descend to the DCKP-type integral form and, via semiclassical limits, yield Poisson automorphisms and explicit Poisson brackets on t...

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