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

Shunsuke Tsuchioka; Masaki Watanabe

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

Representation Theory 2015-11-11 v2 Combinatorics Quantum Algebra

Authors: Shunsuke Tsuchioka , Masaki Watanabe

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 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.

Keywords

pattern avoidance maximal weights affine Lie algebra representations Kashiwara crystal theory module multiplicities

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@article{arxiv.1509.01070,
  title  = {Pattern avoidance seen in multiplicities of maximal weights of affine Lie algebra representations},
  author = {Shunsuke Tsuchioka and Masaki Watanabe},
  journal= {arXiv preprint arXiv:1509.01070},
  year   = {2015}
}

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13 pages

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

Abstract

Keywords

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