The spectrum of the Vladimirov sub-Laplacian on the compact Heisenberg group
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913622253371392 |
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| author | Velasquez-Rodriguez, J. P. |
| author_facet | Velasquez-Rodriguez, J. P. |
| contents | Let $p>2$ be a prime number. In this short note, we calculate explicitly the unitary dual and the matrix coefficients of the Heisenberg group over the $p$-adic integers. As an application, we consider directional Vladimirov-Taibleson derivatives, and some polynomials in these operators. In particular, we calculate explicitly the spectrum of the Vladimirov sub-Laplacian, and show how it provides a non-trivial example of a sub-elliptic operator on compact graded $p$-adic Lie groups. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_07146 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The spectrum of the Vladimirov sub-Laplacian on the compact Heisenberg group Velasquez-Rodriguez, J. P. Representation Theory Let $p>2$ be a prime number. In this short note, we calculate explicitly the unitary dual and the matrix coefficients of the Heisenberg group over the $p$-adic integers. As an application, we consider directional Vladimirov-Taibleson derivatives, and some polynomials in these operators. In particular, we calculate explicitly the spectrum of the Vladimirov sub-Laplacian, and show how it provides a non-trivial example of a sub-elliptic operator on compact graded $p$-adic Lie groups. |
| title | The spectrum of the Vladimirov sub-Laplacian on the compact Heisenberg group |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2401.07146 |