La formule du caract\`ere et la mesure de Plancherel pour les groupes de Lie r\'esolubles unimodulaires sur un corps p-adique

TL;DR

This paper derives a character formula for admissible unitary representations of p-adic solvable groups and computes the Plancherel measure for unimodular cases, advancing harmonic analysis on these groups.

Contribution

It introduces a new character formula for p-adic solvable groups and determines the Plancherel measure in the unimodular setting, filling a gap in representation theory.

Findings

Established a character formula for p-adic solvable groups.

Derived the Plancherel measure for unimodular cases.

Enhanced understanding of harmonic analysis on p-adic groups.

Abstract

We establish a character formula for admissible unitary representations of $p$-adic almost algebraic solvable groups and we deduce the Plancherel measure in the unimodular case.