Crystal structure on King tableaux and semistandard oscillating tableaux

2019/10/10 by Lee, Seung Jin · 2 citations
#05E10 #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1910.04459

Abstract

In 1976, King defined certain tableaux model, called King tableaux in this paper, counting weight multiplicities of irreducible representation of the symplectic group Sp(2m) 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 Q-tableaux in the symplectic version of RSK algorithms. As an application, we discuss Littlewood-Richardson coefficients for Sp(2m) in terms of semistandard oscillating tableaux.

Cited by

• Berele row-insertion and quantum symmetric pairs
• RSK correspondence for King tableaux with Berele insertion

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