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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, W
We 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.


Publication title

Rocky Mountain Journal of Mathematics








School of Natural Sciences


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

Socio-economic Objectives

Expanding knowledge in the mathematical sciences