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

Autor:	Velasquez-Rodriguez, J. P.
Rok vydání:	2024
Předmět:	Mathematics - Representation Theory
Druh dokumentu:	Working Paper
Popis:	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.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2401.07146 Zobrazit plný text záznamu View this record from Arxiv