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arXiv · 2110.07177

Crystal bases of modified $\imath$quantum groups of certain quasi-split types

Hideya Watanabe
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Abstract

In order to see the behavior of $\imath$canonical bases at $q = \infty$, we introduce the notion of $\imath$crystals associated to an $\imath$quantum group of certain quasi-split type. The theory of $\imath$crystals clarifies why $\imath$canonical basis elements are not always preserved under natural homomorphisms. Also, we construct a projective system of $\imath$crystals whose projective limit can be thought of as the $\imath$canonical basis of the modified $\imath$quantum group at $q = \infty$.

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Hideya Watanabe. 2021-10-14. Crystal bases of modified $\imath$quantum groups of certain quasi-split types. https://arxiv.org/abs/2110.07177

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