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

Astrid an Huef, Steven Kaliszewski, Iain Raeburn

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)2344-2357
Number of pages14
JournalJournal of Pure and Applied Algebra
Volume212
Issue number10
DOIs
StatePublished - Oct 2008

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint

Dive into the research topics of 'Covariant representations of Hecke algebras and imprimitivity for crossed products by homogeneous spaces'. Together they form a unique fingerprint.

Cite this