Unitary dual and matrix coefficients of compact nilpotent p-adic Lie groups with dimension $d\le 5$

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发表日期：

2025年2月17日

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J. P. Velasquez-Rodriguez

摘要

Let $p>2$ $p > 2$ be a prime number, and let ${\mathbb {G}}$ $G$ be a compact nilpotent p-adic Lie group with nilpotency class $\mathscr {N}<p$ $N < p$ . In this note, we calculate explicitly the unitary dual and the matrix coefficients of every compact nilpotent p-adic Lie group with dimension less or equal than 5. As an application, we provide the corresponding spectral theorem for the Vladimirov sub-Laplacian, and show how this operator provides a non-trivial example of a globally hypoelliptic operator on compact nilpotent p-adic Lie groups.

Unitary dual and matrix coefficients of compact nilpotent p-adic Lie groups with dimension \(d\le 5\)

摘要