Natural transformations between induction and restriction on iterated wreath product of symmetric group of order 2

2021/06/14 by Mee Seong Im, Im, Mee Seong, Can Ozan Oğuz +1
Mathematics · #16G99 #20B35 (Secondary) #20C30 (Primary) 18N25 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2106.07776

openalex publication_date 2021/06/14 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

Let ℂA_n = ℂ[S₂\wr S₂ \wr⋯ \wr S₂] be the group algebra of n-step iterated wreath product. We prove some structural properties of A_n such as their centers, centralizers, right and double cosets. We apply these results to explicitly write down Mackey theorem for groups A_n and give a partial description of the natural transformations between induction and restriction functors on the representations of the iterated wreath product tower by computing certain hom spaces of the category of \bigoplus_{m≥ 0}(A_m, A_n)-bimodules. A complete description of the category is an open problem.

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