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arXiv · 1810.12475

A Serre presentation for the $\imath$quantum groups

Xinhong Chen·Ming Lu·Weiqiang Wang
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Abstract

Let $(\bf U, \bf U^\imath)$ be a quasi-split quantum symmetric pair of arbitrary Kac-Moody type, where "quasi-split" means the corresponding Satake diagram contains no black node. We give a presentation of the $\imath$quantum group $\bf U^\imath$ with explicit $\imath$Serre relations. The verification of new $\imath$Serre relations is reduced to some new q-binomial identities. Consequently, $\bf U^\imath$ is shown to admit a bar involution under suitable conditions on the parameters.

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BibTeXRIS

Xinhong Chen, Ming Lu, Weiqiang Wang. 2018-10-30. A Serre presentation for the $\imath$quantum groups. https://arxiv.org/abs/1810.12475

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