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An identity for cocycles on coset spaces of locally compact groups

Citation

Dharmadasa, HK and Moran, W, An identity for cocycles on coset spaces of locally compact groups, Rocky Mountain Journal of Mathematics pp. 1-5. ISSN 0035-7596 (2017) [Refereed Article]


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Copyright 2017 the publisher

Official URL: https://projecteuclid.org/euclid.rmjm/1481252487#u...

Abstract

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/HנG satisfying the cocycle identity

λ(x; st)=λ(x.s,t)λ(x,s),a.e.xG/H,s,tG,

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 between cocycles for G/Hx, G/Ky and G/(Hx∩Ky) for almost all x,yG. This also leads to an identity for modular functions of G and the corresponding subgroups.

Item Details

Item Type:Refereed Article
Keywords:separable locally compact groups, quasi-invariant measures, modular function, lambda function
Research Division:Mathematical Sciences
Research Group:Pure Mathematics
Research Field:Lie Groups, Harmonic and Fourier Analysis
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Dharmadasa, HK (Dr Kumudini Dharmadasa)
ID Code:117001
Year Published:2017
Deposited By:Mathematics and Physics
Deposited On:2017-05-26
Last Modified:2018-04-27
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