Crystal bases for the quantum queer superalgebra

2011/03/17 by Dimitar Grantcharov, Ji Hye Jung, Grantcharov, Dimitar +7
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1103.3437

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^{≥ 0}. Our main theorem shows that every U_q(\mathfrak q(n))-module in the category O_int^{≥ 0} has a unique crystal basis.

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• Crystal bases for the quantum queer superalgebra and semistandard decomposition tableaux

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