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

Tsuchioka, Shunsuke; Watanabe, Masaki

doi:10.1090/proc/13597

Pattern avoidance seen in multiplicities of maximal weights of affine Lie algebra representations
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by Shunsuke Tsuchioka and Masaki Watanabe PDF

Proc. Amer. Math. Soc. 146 (2018), 15-28 Request permission

Abstract:

We prove that the multiplicities of certain maximal weights of $\mathfrak {g}(A^{(1)}_{n})$-modules are counted by pattern avoidance on words. This proves and generalizes a conjecture of Jayne-Misra. 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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