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

Let CAn=C[S2≀S2≀⋯≀S2] be the group algebra of an n-step iterated wreath product. We prove some structural properties of An such as their centers, centralizers, and right and double cosets. We apply these results to explicitly write down the Mackey theorem for groups An and give a partial description...

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Bibliographic Details
Published in:Mathematics (Basel) 2022-10, Vol.10 (20), p.3761
Main Authors: Im, Mee Seong, Oğuz, Can Ozan
Format: Article
Language:English
Subjects:
categorification
Frobenius algebras
Group theory
Heisenberg categories
iterated wreath product algebras
Mathematical research
Oil field equipment
Transformations (Mathematics)
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Summary:Let CAn=C[S2≀S2≀⋯≀S2] be the group algebra of an n-step iterated wreath product. We prove some structural properties of An such as their centers, centralizers, and right and double cosets. We apply these results to explicitly write down the Mackey theorem for groups An 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(Am,An)−bimodules. A complete description of the category is an open problem.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10203761