Quasiregular representation

In mathematics, quasiregular 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
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 "quasiregular representation" or modified induced representation.