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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/2401.07146 |
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Table of 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.