Crystal structure on King tableaux and semistandard oscillating tableaux
Combinatorics
2019-10-11 v1 Representation Theory
Abstract
In 1976, King defined certain tableaux model, called King tableaux in this paper, counting weight multiplicities of irreducible representation of the symplectic group for a given dominant weight. Since Kashiwara defined crystals, it is an open problem to provide a crystal structure on King tableaux. In this paper, we present crystal structures on King tableaux and semistandard oscillating tableaux. The semistandard oscillating tableaux naturally appear as -tableaux in the symplectic version of RSK algorithms. As an application, we discuss Littlewood-Richardson coefficients for in terms of semistandard oscillating tableaux.
Cite
@article{arxiv.1910.04459,
title = {Crystal structure on King tableaux and semistandard oscillating tableaux},
author = {Seung Jin Lee},
journal= {arXiv preprint arXiv:1910.04459},
year = {2019}
}