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

Im M. S., OĞUZ C. O.

Mathematics, vol.10, no.20, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 20
  • Publication Date: 2022
  • Doi Number: 10.3390/math10203761
  • Journal Name: Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: categorification, Frobenius algebras, Heisenberg categories, iterated wreath product algebras
  • Galatasaray University Affiliated: Yes

Abstract

Let (Formula presented.) be the group algebra of an n-step iterated wreath product. We prove some structural properties of (Formula presented.) such as their centers, centralizers, and right and double cosets. We apply these results to explicitly write down the Mackey theorem for groups (Formula presented.) 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 (Formula presented.) bimodules. A complete description of the category is an open problem.