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1. La formule du caractère et la formule de Plancherel pour les groupes de Lie résolubles presque connexes sur un corps p-adique

Author

Khemais Maktouf

Subjects
Pure mathematics, Groupe métaplectique, Représentation unitaire, Unitary state, Formule du caractère, Character (mathematics), Méthode de descente, Mathematics::Quantum Algebra, Irreducible representation, Calculus, Groupe résoluble, Orbit method, Element (category theory), Algebraic number, Mathematics::Representation Theory, Analysis, Formule de Plancherel, Mathematics
Abstract

Following Duflo–Vergne (for real reductive groups) and Khalgui–Torasso (for real almost algebraic groups), we prove a Plancherel formula for almost connected solvable p-adic groups ( p ≠ 2 ). To do this, we give a necessary and sufficient condition for a unitary irreducible representation to be admissible in terms of Kirillov–Duflo orbit method. Then we establish a character formula around each semi-simple element.

Published
2012
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