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arXiv · 1103.3437

Crystal bases for the quantum queer superalgebra

Dimitar Grantcharov·Ji Hye Jung·Seok-Jin Kang·Masaki Kashiwara·Myungho Kim
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Abstract

In this paper, we develop the crystal basis theory for the quantum queer superalgebra $U_q(\mathfrak q(n))$. We define the notion of crystal bases and prove the tensor product rule for $U_q(\mathfrak q(n))$-modules in the category $O_int^{\geq 0}$. Our main theorem shows that every $U_q(\mathfrak q(n))$-module in the category $O_int^{\geq 0}$ has a unique crystal basis.

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Dimitar Grantcharov, Ji Hye Jung, Seok-Jin Kang, Masaki Kashiwara, Myungho Kim. 2013-07-13. Crystal bases for the quantum queer superalgebra. https://arxiv.org/abs/1103.3437

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