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arXiv · 2407.06289

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

J. P. Velasquez-Rodriguez
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Abstract

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 $\mathcal{B}_4$.

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J. P. Velasquez-Rodriguez. 2024-07-08. The spectrum of the Vladimirov sub-Laplacian on the compact Engel group. https://arxiv.org/abs/2407.06289

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