Generalized Involution Models for Wreath Products

Abstract

We prove that if a finite group $H$ has a generalized involution model, as defined by Bump and Ginzburg, then the wreath product $H\wr S_n$ also has a generalized involution model. This extends the work of Baddeley concerning involution models for wreath products. As an application, we construct a Gelfand model for wreath products of the form $A\wr S_n$ with $A$ abelian, and give an alternate proof of a recent result due to Adin, Postnikov, and Roichman describing a particularly elegant Gelfand model for the wreath product $\ZZ_r \wr S_n$. We conclude by discussing some notable properties of this representation and its decomposition into irreducible constituents, proving a conjecture of Adin, Roichman, and Postnikov's.

29 pages

References in corpus (1)

• Automorphisms and Generalized Involution Models of Finite Complex Reflection Groups

Cited by in corpus (3)

• Isomorphisms, automorphisms, and generalized involution models
• Gelfand $W$-graphs for classical Weyl groups
• Perfect models for finite Coxeter groups