On the rank varieties of some simple modules for symmetric groups

2024/11/28 by Jialin Wang, Wang, Jialin
Mathematics · #20C20 #20C30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2411.19243

openalex publication_date 2024/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the previous work, Lim and the author determined the rank variety of the simple \mathbbF\mathfrakS_kp-module D(p-1)=D^(kp-p+1,1^p-1) with respect to some maximal elementary abelian p-subgroup E_k and the complexity when k\not≡ 1\pmod p and p is odd. Their method relied on the dimension of the module, which is dependent on k. In this paper, we extend this result to the case for any k≥ 2, and determine the rank variety of D(p-1) and its complexity, providing a proof independent of k.

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