Quasi-regular representation
- Quasi-regular representation
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
:"L"2("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.
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