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arXiv · 2503.11403

Induced Representation of Topological groupoids

K. N. Sridharan·N. Shravan Kumar
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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 $\mu=\{\mu^{u}\}_{u\in G^{0}}$ 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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K. N. Sridharan, N. Shravan Kumar. 2025-03-14. Induced Representation of Topological groupoids. https://arxiv.org/abs/2503.11403

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