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.
ASJC Scopus subject areas
- Algebra and Number Theory