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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.11403 |
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| _version_ | 1866915751357579264 |
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| author | Sridharan, K. N. Kumar, N. Shravan |
| author_facet | Sridharan, K. N. Kumar, N. Shravan |
| contents | 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 $μ=\{μ^{u}\}_{u\in G^{0}}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_11403 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Induced Representation of Topological groupoids Sridharan, K. N. Kumar, N. Shravan Operator Algebras Functional Analysis Primary 18B40, 22A30, Secondary 46L08 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 $μ=\{μ^{u}\}_{u\in G^{0}}$ 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. |
| title | Induced Representation of Topological groupoids |
| topic | Operator Algebras Functional Analysis Primary 18B40, 22A30, Secondary 46L08 |
| url | https://arxiv.org/abs/2503.11403 |