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

Author

Listed:
  • Mee Seong Im

    (Department of Mathematical Sciences, United States Military Academy, West Point, NY 10996, USA
    Department of Mathematics, United States Naval Academy, Annapolis, MD 21402, USA)

  • Can Ozan Oğuz

    (Institute of Information Technologies, Gebze Technical University, İstanbul 41400, Turkey)

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.

Suggested Citation

  • Mee Seong Im & Can Ozan Oğuz, 2022. "Natural Transformations between Induction and Restriction on Iterated Wreath Product of Symmetric Group of Order 2," Mathematics, MDPI, vol. 10(20), pages 1-18, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3761-:d:940458
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