Distributions a support compact et representations unitaires
Dominique Manchon

TL;DR
This paper investigates properties of certain unitary representations of Lie groups, showing conditions under which associated operators are regularizing or trace class, and extending character formulas to specific distributions.
Contribution
It introduces conditions for regularizing and trace properties of operators linked to unitary representations and extends character formulas to new classes of distributions.
Findings
Operators are regularizing when wavefront sets do not intersect.
Operators are trace class under certain conditions.
Character formulas are extended to specific distributions.
Abstract
Dans cet article nous precisons les notions de representations unitaires fortement tracables et de front d'onde d'une representation unitaire, toutes deux introduites par Roger Howe. Nous montrons que pour toute distribution a support compact sur un groupe de Lie connexe dont le front d'onde ne rencontre pas l'oppose du front d'onde de la representation l'operateur est regularisant. De plus, sous les memes hypotheses cet operateur est a trace si la representation est fortement tracable. Dans le cas ou la representation est irreductible et associee par la methode des orbites a une orbite fermee et temperee, nous montrons qu'elle est fortement tracable et nous etendons la formule des caracteres aux operateurs pour les distributions a support compact dont le front d'onde verifie la condition de transversalite ci-dessus.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Geometry and complex manifolds
