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arXiv · 2407.13127

PBW bases for $\imath$quantum groups

Ming Lu·Ruiqi Yang·Weinan Zhang
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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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Ming Lu, Ruiqi Yang, Weinan Zhang. 2024-07-18. PBW bases for $\imath$quantum groups. https://arxiv.org/abs/2407.13127

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