Jacob Bradd

activity

20232025

collaborators

4 papers

math.RT2025

Lie groupoids, the Satake compactification and the tempered dual, I: The Satake groupoid

Jacob Bradd, Nigel Higson, Robert Yuncken

The (maximal) Satake compactification associated to a real reductive group $G$ is the closure of the symmetric space of all maximal compact subgroups of $G$ within the compact spac…

math.RT2025

Lie groupoids, the Satake compactification and the tempered dual, II: The Harish-Chandra principle

Jacob Bradd, Nigel Higson, Robert Yuncken

We give a geometric account of Harish-Chandra's principle that a tempered irreducible representation of a real reductive group is either square-integrable modulo center, or embedda…

math.RT2024

Operator K-Theory and Tempiric Representations

Jacob Bradd, Nigel Higson, Robert Yuncken

David Vogan proved that if $G$ is a real reductive group, and if $K$ is a maximal compact subgroup of $G$ , then every irreducible representation of $K$ is included as a minimal $K$ …

math.OA2023

Compatible Decomposition of the Casselman Algebra and the Reduced Group C*-algebra of a Real Reductive Group

Jacob Bradd

For a real reductive group $G$ , we investigate the structure of the Casselman algebra $S (G)$ and its similarities to the structure of the reduced group $C^{*}$ -algebra $C_r…