TY - JOUR

T1 - Covariant representations of Hecke algebras and imprimitivity for crossed products by homogeneous spaces

AU - an Huef, Astrid

AU - Kaliszewski, Steven

AU - Raeburn, Iain

N1 - Funding Information:
This research was supported by grants from the Australian Research Council, the National Science Foundation and the University of New South Wales.

PY - 2008/10

Y1 - 2008/10

N2 - 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.

AB - 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.

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U2 - 10.1016/j.jpaa.2008.03.011

DO - 10.1016/j.jpaa.2008.03.011

M3 - Article

AN - SCOPUS:44649119850

VL - 212

SP - 2344

EP - 2357

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 10

ER -