Quasi-regular representation

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In mathematics, quasi-regular representation is a concept of representation theory, for a locally compact group G and a homogeneous space G\H where H is a closed subgroup.

In line with the concepts of regular representation and induced representation, G acts on functions on G\H. If however Haar measures give rise only to a quasi-invariant measure on G\H, certain 'correction factors' have to be made to the action on functions, for

L²(G\H)

to afford a unitary representation of G on square-integrable functions. With appropriate scaling factors, therefore, introduced into the action of G, this is the quasi-regular representation or modified induced representation.