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Generalized involution models for wreath products

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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 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 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 r ≀ S 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.

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  1. Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139-4307, USA

    Eric Marberg

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  1. Eric Marberg
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Correspondence to Eric Marberg.

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Marberg, E. Generalized involution models for wreath products. Isr. J. Math. 192, 157–195 (2012). https://doi.org/10.1007/s11856-012-0021-4

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  • DOI: https://doi.org/10.1007/s11856-012-0021-4

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