Unitary dual and matrix coefficients of compact nilpotent p-adic Lie groups with dimension $d \leq 5$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910758942539776 |
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| author | Velasquez-Rodriguez, J. P. |
| author_facet | Velasquez-Rodriguez, J. P. |
| contents | Let p> 2 be a prime number, and let G be a compact nilpotent p-adic Lie group with nilpotency class N<p. In this note we calculate explicitly the unitary dual and the matrix coefficients of every compact nilpotent-adic Lie group with dimension less or equal than 5. As an application, we provide the corresponding spectral theorem for the Vladimirov sub-Laplacian, and show how this operator provides a non-trivial example of a globally hypoelliptic operator on compact nilpotent p-adic Lie groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16498 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unitary dual and matrix coefficients of compact nilpotent p-adic Lie groups with dimension $d \leq 5$ Velasquez-Rodriguez, J. P. Representation Theory Let p> 2 be a prime number, and let G be a compact nilpotent p-adic Lie group with nilpotency class N<p. In this note we calculate explicitly the unitary dual and the matrix coefficients of every compact nilpotent-adic Lie group with dimension less or equal than 5. As an application, we provide the corresponding spectral theorem for the Vladimirov sub-Laplacian, and show how this operator provides a non-trivial example of a globally hypoelliptic operator on compact nilpotent p-adic Lie groups. |
| title | Unitary dual and matrix coefficients of compact nilpotent p-adic Lie groups with dimension $d \leq 5$ |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2412.16498 |