Natural Transformations between Induction and Restriction on Iterated Wreath Product of Symmetric Group of Order 2

Mee Seong Im () and Can Ozan Oğuz
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Mee Seong Im: Department of Mathematical Sciences, United States Military Academy, West Point, NY 10996, USA
Can Ozan Oğuz: Institute of Information Technologies, Gebze Technical University, İstanbul 41400, Turkey

Mathematics, 2022, vol. 10, issue 20, 1-18

Abstract: Let C A n = C [ S 2 ≀ S 2 ≀ ⋯ ≀ S 2 ] be the group algebra of an n -step iterated wreath product. We prove some structural properties of A n such as their centers, centralizers, and right and double cosets. We apply these results to explicitly write down the 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 ⨁ m ≥ 0 ( A m , A n ) − bimodules. A complete description of the category is an open problem.

Keywords: Heisenberg categories; categorification; Frobenius algebras; iterated wreath product algebras (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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