Covariant representations of Hecke algebras and imprimitivity for crossed products by homogeneous spaces |
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Authors: | Astrid an Huef Iain Raeburn |
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Institution: | a School of Mathematics and Statistics, The University of New South Wales, NSW 2052, Australia b Department of Mathematics and Statistics, Arizona State University, AZ 85287-1804, USA c School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia |
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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 ?2(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. |
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Keywords: | Primary 46L55 secondary 20C08 |
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