Pattern avoidance seen in multiplicities of maximal weights of affine Lie algebra representations
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- by Shunsuke Tsuchioka and Masaki Watanabe PDF
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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.References
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Additional Information
- Shunsuke Tsuchioka
- Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, Komaba, Meguro, Tokyo, 153-8914, Japan
- MR Author ID: 823219
- Email: tshun@kurims.kyoto-u.ac.jp
- Masaki Watanabe
- Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, Komaba, Meguro, Tokyo, 153-8914, Japan
- MR Author ID: 1095668
- Email: mwata@ms.u-tokyo.ac.jp
- Received by editor(s): November 10, 2015
- Received by editor(s) in revised form: October 12, 2016
- Published electronically: September 28, 2017
- Additional Notes: The first author was supported in part by JSPS Kakenhi Grants 26800005.
- Communicated by: Kailash C. Misra
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 15-28
- MSC (2010): Primary 17B67; Secondary 05A05
- DOI: https://doi.org/10.1090/proc/13597
- MathSciNet review: 3723117