PATTERN AVOIDANCE SEEN IN MULTIPLICITIES OF MAXIMAL WEIGHTS OF AFFINE LIE ALGEBRA REPRESENTATIONS

被引：5
|
作者：
Tsuchioka, Shunsuke [1 ]
Watanabe, Masaki [1 ]
机构：
[1] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, Tokyo 1538914, Japan
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2018年 / 146卷 / 01期
关键词：
Weight multiplicities; affine Lie algebras; pattern avoidance; maximal weights; Kashiwara's crystal; Littelmann's path model; RSK correspondence; plane partitions; orbit Lie algebras; quantum binomial coefficients; categorification; Hecke algebras; symmetric groups; modular representation theory; Mullineux involution;
D O I：
10.1090/proc/13597
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that the multiplicities of certain maximal weights of g(A(n)((1)))-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(2n)((2)) and D-n+(1(2)). Both proofs are applications of Kashiwara's crystal theory.
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页码：15 / 28
页数：14
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