Factorization of Lie group representations and the Helgason conjecture

Date/heure
5 mars 2026
14:15 - 15:15

Lieu
Salle de séminaires Metz

Oratrice ou orateur
Heiko Gimperlein (Innsbruck)

Catégorie d'évènement
Séminaire Théorie de Lie, Géométrie et Analyse


Résumé

We discuss factorization problems for representations of a real Lie group G. First we discuss a factorization theorem of Dixmier-Malliavin type for the space of analytic vectors $E^{\omega}$ for representations of G on, for example, a Banach space E: There exists a natural algebra of superexponentially decreasing analytic functions A(G), such that $E^{\omega} = A(G) * E^{\omega}$. Such theorems can be deduced from simple properties of the wave equation on G, which provides detailed information about functions of the Laplacian. We then formulate a factorization theorem for real reductive groups which implies the Helgason conjecture, and we outline a new and elementary proof. (joint work with Krötz and Lienau, resp. Krötz, Kuit and Schlichtkrull)