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arXiv · 1704.01277

Crystal basis theory for a quantum symmetric pair $(\mathbf{U},\mathbf{U}^{\jmath})$

Hideya Watanabe
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Abstract

We study the representation theory of a quantum symmetric pair $(\mathbf{U},\mathbf{U}^{\jmath})$ with two parameters $p,q$ of type AIII, by using highest weight theory and a variant of Kashiwara's crystal basis theory. Namely, we classify the irreducible $\mathbf{U}^{\jmath}$-modules in a suitable category and associate with each of them a basis at $p=q=0$, the $\jmath$-crystal basis. The $\jmath$-crystal bases have nice combinatorial properties as the ordinary crystal bases do.

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Hideya Watanabe. 2017-04-05. Crystal basis theory for a quantum symmetric pair $(\mathbf{U},\mathbf{U}^{\jmath})$. https://arxiv.org/abs/1704.01277

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