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

Astrid an Huef·S. Kaliszewski·Iain Raeburn
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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 $c_0(G/H)$ 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 $c_0(G/H)$ which are multiples of the multiplication representation on $\ell^2(G/H)$, 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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Astrid an Huef, S. Kaliszewski, Iain Raeburn. 2005-09-13. Covariant representations of Hecke algebras and imprimitivity for crossed products by homogeneous spaces. https://arxiv.org/abs/math/0509291

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