Square-integrability modulo a subgroup

TL;DR

This paper introduces a new proof of the Imprimitivity theorem and defines square-integrable representations modulo a subgroup, clarifying their connection to coherent states, wavelet transforms, and covariant localization.

Contribution

It provides a novel proof of the Imprimitivity theorem and a new definition of square-integrable representations modulo a subgroup, enhancing understanding of their interrelations.

Findings

New proof of Imprimitivity theorem for transitive systems of covariance

Definition of square-integrable representation modulo a subgroup

Clarification of relations between coherent states, wavelet transforms, and covariant localization

Abstract

A new proof of Imprimitivity theorem for transitive systems of covariance is given and a definition of square-integrable representation modulo a subgroup is proposed. This clarifies the relation between coherent states, wavelet transforms and covariant localisation observables.