Date/heure
18 septembre 2025
14:15 - 15:15
Oratrice ou orateur
Pierre Clare (William & Mary)
Catégorie d'évènement Séminaire Théorie de Lie, Géométrie et Analyse
Résumé
The phenomenon known as ‘the Mackey analogy’ is a correspondance between the tempered dual of a Lie group $G$ and the unitary dual of its associated motion group $G_0$. The precise statement, formulated and proven by Higson in the case of complex groups, and by Afgoustidis in the general case of real groups, has long been known to be intimately connected to the Connes-Kasparov isomorphism relating the K-theory of the reduced C$^\ast$-algebras of $G$ and $G_0$ via a deformation argument.
In this talk, I will report on joint work with Higson and Román, aimed at understanding the Mackey analogy directly at the level of the group C$^\ast$-algebras. The main result is an embedding of the C$^\ast$-algebra of $G_0$ into the reduced C$^\ast$-algebra of $G$, which is proven to characterize the bijection of Afgoustidis and to induce the Connes-Kasparov isomorphism.