Lusztig data of Kashiwara-Nakashima tableaux in types B and C

2016/10/09 by Kwon, Jae-Hoon
#05E10 #17B37 #22E46 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1610.02640

Abstract

We provide an explicit combinatorial description of the embedding of the crystal of Kashiwara-Nakashima tableaux in types B and C into that of \bi-Lusztig data associated to a family of reduced expressions \bi of the longest element w₀. The description of the embedding is simple and elementary using only the Schützenberger's jeu de taquin and RSK algorithm. A spinor model for classical crystals plays an important role as an intermediate object connecting Kashiwara-Nakashima tableaux and Lusztig data.

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