Pattern avoidance seen in multiplicities of maximal weights of affine Lie algebra representations

2015/09/03 by Tsuchioka, Shunsuke, Watanabe, Masaki
#Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1509.01070

Abstract

We prove that the multiplicities of certain maximal weights of \mathfrakg(A⁽¹⁾_n)-modules are counted by pattern avoidance on words. This proves and generalizes a conjecture of Misra-Rebecca. We also prove similar phenomena in types A⁽²⁾_2n and D⁽²⁾_n+1. Both proofs are applications of Kashiwara's crystal theory.

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