Induced Representation of Topological groupoids

2025/03/14 by Karthik Sridharan, Sridharan, K. N., N. Shravan Kumar +1 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Homotopy and Cohomology in Algebraic Topology #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2503.11403

Abstract

Let G be a locally compact second countable groupoid with a Haar system. In this article, we introduce the induced representation of G from a continuous unitary representation of a closed wide subgroupoid H with a Haarsystem provided there exists a full equivariant system of measures μ=\μ^u\_{u∈ G⁰} on G/H. We prove some basic properties of induced representation and a theorem on induction in stages. A groupoid version of Mackey's tensor product theorem is also provided. We also prove a groupoid version of Frobenius Reciprocity theorem on compact transitive groupoids.

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• Weak containment of representation on topological groupoids

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