Quasiregular representation

For other uses, see Quasiregular.

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

1. ↑ Ghorbel, Amira; Hamrouni, Hatem (2017). "Quasi-regular Representations of Two-Step Nilmanifolds". in Baklouti, Ali; Nomura, Takaaki (in en). Cham: Springer International Publishing. pp. 137–155. doi:10.1007/978-3-319-65181-1_5. ISBN 978-3-319-65181-1. https://link.springer.com/chapter/10.1007/978-3-319-65181-1_5.

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