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A Serre presentation for the $\imath$quantum covering groups (1912.09281v1)

Published 17 Dec 2019 in math.RT

Abstract: Let $(\mathbf{U}, \mathbf{U}\imath)$ be a quasi-split quantum symmetric pair of Kac-Moody type. The $\imath$quantum group $\mathbf{U}\imath$ admits a Serre presentation featuring the $\imath$-Serre relations in terms of $\imath$-divided powers. Generalizing this result, we give a Serre presentation $ \mathbf{U}\imath_\pi $ of quantum symmetric pairs $ (\mathbf{U}\pi, \mathbf{U}\imath\pi) $ for quantum covering algebras $\mathbf{U}\pi$, which have an additional parameter $ \pi $ that specializes to the Lusztig quantum group when $ \pi = 1 $ and quantum supergroups of anisotropic type when $ \pi = -1 $. We give a Serre presentation for $ \mathbf{U}\imath\pi $, introducing the $\imath\pi$-Serre relations and $\imath\pi$-divided powers.

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