The spectrum of the Vladimirov sub-Laplacian on the compact Engel group

Let \(p>3\) be a prime number. In this note, we 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...

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Bibliographic Details
Published in:arXiv.org 2024-07
Main Author: Velasquez-Rodriguez, J P
Format: Article
Language:English
Subjects:
Prime numbers
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Summary:Let \(p>3\) be a prime number. In this note, we 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 \(\mathcal{B}_4\).
ISSN:2331-8422