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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.06289 |
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| _version_ | 1866917875860635648 |
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| author | Velasquez-Rodriguez, J. P. |
| author_facet | Velasquez-Rodriguez, J. P. |
| contents | Let $p>3$ be a prime number. In this note, we use p-adic Gaussian integrals to calculate explicitly the unitary dual and the matrix coefficients of the Engel group over the $p$-adic integers $\mathcal{B}_4(\mathbb{Z}_p)$. We use this information to calculate explicitly the spectrum of the Vladimirov sub-Laplacian, and show how it defines a globally hypoelliptic operator on $\mathcal{B}_4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06289 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The spectrum of the Vladimirov sub-Laplacian on the compact Engel group Velasquez-Rodriguez, J. P. Representation Theory Let $p>3$ be a prime number. In this note, we use p-adic Gaussian integrals to calculate explicitly the unitary dual and the matrix coefficients of the Engel group over the $p$-adic integers $\mathcal{B}_4(\mathbb{Z}_p)$. We use this information to calculate explicitly the spectrum of the Vladimirov sub-Laplacian, and show how it defines a globally hypoelliptic operator on $\mathcal{B}_4$. |
| title | The spectrum of the Vladimirov sub-Laplacian on the compact Engel group |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2407.06289 |