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.^[1]

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 quasiregular representation or modified induced representation.

References

^ Ghorbel, Amira; Hamrouni, Hatem (2017). Baklouti, Ali; Nomura, Takaaki (eds.). Quasi-regular Representations of Two-Step Nilmanifolds. Cham: Springer International Publishing. pp. 137–155. doi:10.1007/978-3-319-65181-1_5. ISBN 978-3-319-65181-1.

[1] Ghorbel, Amira; Hamrouni, Hatem (2017). Baklouti, Ali; Nomura, Takaaki (eds.). Quasi-regular Representations of Two-Step Nilmanifolds. Cham: Springer International Publishing. pp. 137–155. doi:10.1007/978-3-319-65181-1_5. ISBN 978-3-319-65181-1.

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