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# An identity for cocycles on coset spaces of locally compact groups

journal contribution

posted on 2023-05-20, 00:59 authored by Hettiarachchilae DharmadasaHettiarachchilae Dharmadasa, Moran, WWe prove here an identity for cocycles associated with homogeneous spaces in the context of locally compact groups. Mackey introduced cocycles (λ-functions) in his work on representation theory of such groups. For a given locally compact group G and a closed subgroup H of G, with right coset space G/H, a cocycle λ is a real-valued Borel function on G/H × G satisfying the cocycle identity λ(x, st) = λ(x.s, t)λ(x, s), almost everywhere x ∈ G/H, s, t ∈ G, where the “almost everywhere” is with respect to a measure whose null sets pull back to Haar measure null sets on G. Let H and K be regularly related closed subgroups of G. Our identity describes a relationship among cocycles for G/Hx, G/Ky and G/(Hx ∩ Ky) for almost all x, y ∈ G. This also leads to an identity for modular functions of G and the corresponding subgroups.

## History

## Publication title

Rocky Mountain Journal of Mathematics## Volume

48## Pagination

269-277## ISSN

0035-7596## Department/School

School of Natural Sciences## Publisher

Rocky Mt Math Consortium## Place of publication

Ariz State Univ, Dept Math, Tempe, USA, Az, 85287-1904## Rights statement

Copyright 2018 Rocky Mountain Mathematics Consortium## Repository Status

- Restricted