Imprimitivity theorem for groupoid representations

TL;DR

This paper generalizes Mackey's imprimitivity theorem to locally compact transitive topological groupoids, establishing a framework for understanding groupoid representations induced by isotropy subgroupoid representations.

Contribution

It introduces and proves an imprimitivity theorem for groupoid representations, extending classical results from group theory to the more general setting of topological groupoids.

Findings

Established the imprimitivity theorem for transitive topological groupoids.

Connected groupoid representations with isotropy subgroupoid representations.

Generalized Mackey's theorem to a broader mathematical context.

Abstract

We define and investigate the concept of the groupoid representation induced by a representation of the isotropy subgroupoid. Groupoids in question are locally compact transitive topological groupoids. We formulate and prove the imprimitivity theorem for such representations which is a generalization of the classical Mackey's theorem known from the theory of group representations.