Generalized involution models for wreath products
Author(s)Marberg, Eric Paul
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Israel Journal of Mathematics
Marberg, Eric. “Generalized Involution Models for Wreath Products.” Israel Journal of Mathematics 192.1 (2012): 157–195.
Author's final manuscript