On Gelfand pairs associated to transitive groupoids
| Autor: | Kinvi Kangni, Ibrahima Toure |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Discrete mathematics
Transitive relation General Mathematics lcsh:T57-57.97 Hausdorff space Second-countable space groupoid representation Characterization (mathematics) Gelfand pair Convolution Combinatorics Gelfand pairs Mathematics::Category Theory lcsh:Applied mathematics. Quantitative methods Locally compact space Commutative property Mathematics transitive groupoids |
| Zdroj: | Opuscula Mathematica, Vol 33, Iss 4, Pp 751-762 (2013) |
| ISSN: | 1232-9274 |
| Popis: | Let \(G\) be a topological locally compact, Hausdorff and second countable groupoid with a Haar system and \(K\) a compact subgroupoid of \(G\) with a Haar system too. \((G,K)\) is a Gelfand pair if the algebra of bi-\(K\)-invariant functions is commutative under convolution. In this paper, we give a characterization of Gelfand pairs associated to transitive groupoids which generalize a well-known result in the groups case. Using this result, we prove that the study of Gelfand pairs associated to transitive groupoids is equivalent to that of Gelfand pairs associated to its isotropy groups. |
| Databáze: | OpenAIRE |
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