Generalized involution models for wreath products
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Author(s)
Marberg, Eric Paul
Date Issued
February 2012
Journal
Israel Journal of Mathematics
Publisher
Springer-Verlag
Citation
Marberg, Eric. “Generalized Involution Models for Wreath Products.” Israel Journal of Mathematics 192.1 (2012): 157–195.
Version
Author's final manuscript
Abstract
We prove that if a finite group H has a generalized involution model, as defined by Bump and Ginzburg, then the wreath product H ≀ S[subscript n] also has a generalized involution model. This extends the work of Baddeley concerning involution models for wreath products. As an application, we construct a Gel’fand model for wreath products of the form A ≀ S[subscript n] with A abelian, and give an alternate proof of a recent result due to Adin, Postnikov and Roichman describing a particularly elegant Gel’fand model for the wreath product ℤ[subscript r] ≀ S[subscript n]. We conclude by discussing some notable properties of this representation and its decomposition into irreducible constituents, proving a conjecture of Adin, Postnikov and Roichman.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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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.
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DOI of Published Version
https://doi.org/10.1007/s11856-012-0021-4
