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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 is the closure of the symmetric space of all maximal compact subgroups of 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.RT2025
A Mackey embedding for reduced C*-algebras of real reductive groups
Pierre Clare, Nigel Higson, Angel Román
The purpose of this paper is construct an embedding of the C*-algebra of the Cartan motion group of a real reductive group G into the reduced C*-algebra of G itself. The embedding…