Covariant representations of Hecke algebras and imprimitivity for crossed products by homogeneous spaces

2005/09/13 by Astrid an Huef, S. Kaliszewski, Huef, Astrid an +3
Mathematics · #20C08 #46L55 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Operator Algebras (math.OA) #Random Matrices and Applications #math.OA #msc:20C08 #msc:46L55

paper · pdf · doi:10.48550/arxiv.math/0509291

20 pages

arxiv created 2005/09/13 · openalex publication_date 2005/09/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For discrete Hecke pairs (G,H), we introduce a notion of covariant representation which reduces in the case where H is normal to the usual definition of covariance for the action of G/H on c₀(G/H) by right translation; in many cases where G is a semidirect product, it can also be expressed in terms of covariance for a semigroup action. We use this covariance to characterise the representations of c₀(G/H) which are multiples of the multiplication representation on ℓ²(G/H), and more generally, we prove an imprimitivity theorem for regular representations of certain crossed products by coactions of homogeneous spaces. We thus obtain new criteria for extending unitary representations from H to G.

Citations

• Extension problems for representations of crossed-product C*-algebras

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