MIT Libraries logoDSpace@MIT

MIT
View Item 
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Hopf Modules and Representations of Finite Wreath Products

Author(s)
Shelley-Abrahamson, Seth
Thumbnail
Download10468_2016_9633_ReferencePDF.pdf (206.8Kb)
PUBLISHER_POLICY

Publisher Policy

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.

Terms of use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Metadata
Show full item record
Abstract
For a finite group G and nonnegative integer n ≥ 0, one may consider the associated tower G≀S[subscript n]:=S[subscript n]⋉G[superscript n] of wreath product groups. Zelevinsky associated to such a tower the structure of a positive self-adjoint Hopf algebra (PSH-algebra) R(G) on the direct sum over integers n ≥ 0 of the Grothendieck groups K[subscript 0](Rep−G≀S[subscript n]). In this paper, we study the interaction via induction and restriction of the PSH-algebras R(G) and R(H) associated to finite groups H ⊂ G. A class of Hopf modules over PSH-algebras with a compatibility between the comultiplication and multiplication involving the Hopf k[superscript th]-power map arise naturally and are studied independently. We also give an explicit formula for the natural PSH-algebra morphisms R(H) → R(G) and R(G) → R(H) arising from induction and restriction. In an appendix, we consider a family of subgroups of wreath product groups analogous to the subgroups G(m, p, n) of the wreath product cyclotomic complex reflection groups G(m, 1, n).
Date issued
2016-06
URI
http://hdl.handle.net/1721.1/107447
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Algebras and Representation Theory
Publisher
Springer Netherlands
Citation
Shelley-Abrahamson, Seth. “Hopf Modules and Representations of Finite Wreath Products.” Algebras and Representation Theory 20, no. 1 (June 29, 2016): 123–145.
Version: Author's final manuscript
ISSN
1386-923X
1572-9079

Collections
  • MIT Open Access Articles

Browse

All of DSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

Login

Statistics

OA StatisticsStatistics by CountryStatistics by Department
MIT Libraries
PrivacyPermissionsAccessibilityContact us
MIT
Content created by the MIT Libraries, CC BY-NC unless otherwise noted. Notify us about copyright concerns.