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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…
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…
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…
Pseudodifferential operators and the Connes-Kasparov isomorphism
Peter DeBello, Nigel Higson
We compute the K-theory of the C*-category generated by order zero, equivariant, properly supported, classical pseudodifferential operators acting on sections of homogeneous bundle…