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- Title
Natural Transformations between Induction and Restriction on Iterated Wreath Product of Symmetric Group of Order 2.
- Authors
Im, Mee Seong; Oğuz, Can Ozan
- 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.
- Subjects
GROUP algebras; FROBENIUS algebras; C*-algebras; WREATH products (Group theory)
- Publication
Mathematics (2227-7390), 2022, Vol 10, Issue 20, p3761
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math10203761