Lakshmibai-Seshadri paths and non-symmetric Cauchy identity

2016/11/30 by Choi, Seung-Il, Kwon, Jae-Hoon · 1 citation
#05E10 #17B37 #22E46 #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1611.10089

Abstract

We give a simple crystal theoretic interpretation of the Lascoux's expansion of a non-symmetric Cauchy kernel ∏_{i+ j≤ n+1}(1-x_iy_j)^-1, which is given in terms of Demazure characters and atoms. We give a bijective proof of the non-symmetric Cauchy identity using the crystal of Lakshmibai-Seshadri paths, and extend it to the case of continuous crystals.

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• A Local Characterization of Unions of Demazure Crystals

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