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arXiv · 1103.1456

Crystal bases for the quantum queer superalgebra and semistandard decomposition tableaux

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

In this paper, we give an explicit combinatorial realization of the crystal B(λ) for an irreducible highest weight U_q(q(n))-module V(λ) in terms of semistandard decomposition tableaux. We present an insertion scheme for semistandard decomposition tableaux and give algorithms of decomposing the tensor product of q(n)-crystals. Consequently, we obtain explicit combinatorial descriptions of the shifted Littlewood-Richardson coefficients.

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Dimitar Grantcharov, Ji Hye Jung, Seok-Jin Kang, Masaki Kashiwara, Myungho Kim. 2013-07-14. Crystal bases for the quantum queer superalgebra and semistandard decomposition tableaux. https://arxiv.org/abs/1103.1456

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