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

Abstract

We prove that the multiplicities of certain maximal weights of $\mathfrak{g}(A_n^{(1)})$-modules are counted by pattern avoidance on words. This proves and generalizes a conjecture of Misra-Rebecca. We also prove similar phenomena in types $A_{2n}^{(2)}$ and $D_{n+1}^{(2)}$. Both proofs are applications of Kashiwara's crystal theory.

13 pages

References in corpus (1)

• Blocks of cyclotomic Hecke algebras

Cited by in corpus (1)

• Representation type for block algebras of Hecke algebras of classical type