Date/heure
10 octobre 2024
14:15 - 15:15
Oratrice ou orateur
Jacob Bradd
Catégorie d'évènement Séminaire Théorie de Lie, Géométrie et Analyse
Résumé
I will talk about a refinement of the Connes-Kasparov isomorphism, which is proved by understanding the structure of the Casselman algebra of rapidly decreasing functions on a real reductive group. I show that this Casselman algebra, which encodes nonunitary representation theory, and the reduced group C^*-algebra, which encodes tempered unitary representation theory, are built in very similar ways from similar elementary components. The structure of the Casselman algebra is understood using techniques from Delorme’s proof of the Paley-Wiener theorem for real reductive groups, which describes the Fourier transform of compactly supported smooth functions. Thanks to the similar structures of the two algebras, it becomes straightforward to prove that the two algebras, once cut down to certain finite sets of K-types, have isomorphic K-theory, which is the refinement of Connes-Kasparov. This work is essentially my thesis at Penn State.