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Crystal Bases for the Quantum Superalgebra $U_q(gl(m,n))$

Georgia Benkart·Seok-Jin Kang·Masaki Kashiwara
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Abstract

We develop a crystal base theory for the general linear Lie superalgebra $gl(m,n)$. We prove that any irreducible $U_q(gl(m,n))$-module in some category has a crystal base, and prove that its associated crystal base is parameterized by semistandard tableaux.

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Georgia Benkart, Seok-Jin Kang, Masaki Kashiwara. 1998-10-15. Crystal Bases for the Quantum Superalgebra $U_q(gl(m,n))$. https://arxiv.org/abs/math/9810092

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