莫线对合和晶体同构

IF 0.9 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A Pub Date : 2023-09-14 DOI:10.5070/c63261986

Nicolas Jacon

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引用次数: 1

摘要

利用晶体同构的概念和\(A\)型仿射Hecke代数的Iwahori-Matsumoto对合，提出了计算对称群及其Hecke代数的Mullineux对合的新方法。因此，我们得到了几种新的计算初等组合算法，其中一种算法等价于Xu算法(即Mullineux原始算法)。因此，我们得到了这些算法的一个简单的解释和一个新的初等证明，证明它们确实计算了Mullineux对合。关键词:对称群，莫线对合，晶体图

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Mullineux involution and crystal isomorphisms

We develop a new approach for the computation of the Mullineux involution for the symmetric group and its Hecke algebra using the notion of crystal isomorphism and the Iwahori-Matsumoto involution for the affine Hecke algebra of type \(A\). As a consequence, we obtain several new elementary combinatorial algorithms for its computation, one of which is equivalent to Xu algorithm (and thus Mullineux original algorithm). We thus obtain a simple interpretation of these algorithms and a new elementary proof that they indeed compute the Mullineux involution.Mathematics Subject Classifications: 20C08, 05E10Keywords: Symmetric group, Mullineux involution, crystal graph

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来源期刊

Journal of Combinatorial Theory Series A 数学-数学

CiteScore

2.90

自引率

9.10%

发文量

审稿时长

12 months

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research concerned with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series A is concerned primarily with structures, designs, and applications of combinatorics and is a valuable tool for mathematicians and computer scientists.