Crystal bases for the quantum queer superalgebra and semistandard decomposition tableaux

Grantcharov, Dimitar; Jung, Ji Hye; Kang, Seok-Jin; Kashiwara, Masaki; Kim, Myungho

doi:10.1090/S0002-9947-2013-05866-7

Crystal bases for the quantum queer superalgebra and semistandard decomposition tableaux
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by Dimitar Grantcharov, Ji Hye Jung, Seok-Jin Kang, Masaki Kashiwara and Myungho Kim PDF

Trans. Amer. Math. Soc. 366 (2014), 457-489 Request permission

Abstract:

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

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