Crystal bases for the quantum queer superalgebra and semistandard decomposition tableaux
Representation Theory
2013-07-16 v2 Quantum Algebra
Abstract
In this paper, we give an explicit combinatorial realization of the crystal B(\lambda) for an irreducible highest weight U_q(q(n))-module V(\lambda) 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.
Keywords
Cite
@article{arxiv.1103.1456,
title = {Crystal bases for the quantum queer superalgebra and semistandard decomposition tableaux},
author = {Dimitar Grantcharov and Ji Hye Jung and Seok-Jin Kang and Masaki Kashiwara and Myungho Kim},
journal= {arXiv preprint arXiv:1103.1456},
year = {2013}
}
Comments
38 pages, small change on acknowledgement