28 citations · 49 across the 10 of their papers we have counts for
14 papers
Reduced C*-algebras and K-theory for reductive -adic groups
Pierre Clare, Tyrone Crisp
We calculate the -theory of the reduced -algebra of a reductive -adic group . To do so, we show that each direct summand in Plymen's Plancherel decompositi…
The Mackey bijection as a stratified equivalence
Alexandre Afgoustidis, Pierre Clare
This paper is about the Mackey analogy between the tempered representation theory of a real reductive group and that of its Cartan motion group. We consider the embedding of reduce…
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…
Noncommutative distances on graphs: An explicit approach via Birkhoff-James orthogonality
Pierre Clare, Chi-Kwong Li, Edward Poon +1
We study the problem of calculating noncommutative distances on graphs, using techniques from linear algebra, specifically, Birkhoff-James orthogonality. A complete characterizatio…
On the Connes-Kasparov isomorphism, II: The Vogan classification of essential components in the tempered dual
Pierre Clare, Nigel Higson, Yanli Song
This is the second of two papers dedicated to the computation of the reduced C*-algebra of a connected, linear, real reductive group up to C*-algebraic Morita equivalence, and the…
On the Connes-Kasparov isomorphism, I: The reduced C*-algebra of a real reductive group and the K-theory of the tempered dual
Pierre Clare, Nigel Higson, Yanli Song +1
This is the first of two papers dedicated to the computation of the reduced C*-algebra of a connected, linear, real reductive group up to Morita equivalence, and the verification o…
C*-algebraic normalization and Godement-Jacquet factors
Pierre Clare
We observe how certain distribution on that generates Godement-Jacquet -factors appears naturally in the C*-algebraic normalization process for standard intertw…
Invariant trilinear forms for spherical degenerate principal series of complex symplectic groups
Pierre Clare
We compute generalized Bernstein-Reznikov integrals associated with standard complex symplectic forms by studying Knapp-Stein intertwining operators between spherical degenerate pr…
Adjoint functors between categories of Hilbert C*-modules
Pierre Clare, Tyrone Crisp, Nigel Higson
Let E be a (right) Hilbert C*-module over a C*-algebra A. If E is equipped with a left action of a second C*-algebra B, then tensor product with E gives rise to a functor from the…
Parabolic induction and restriction via C*-algebras and Hilbert C*-modules
Pierre Clare, Tyrone Crisp, Nigel Higson
This paper is about the reduced group C*-algebras of real reductive groups, and about Hilbert C*-modules over these C*-algebras. We shall do three things. First we shall apply theo…
C*-algebraic intertwiners for degenerate principal series of special linear groups
Pierre Clare
We construct unitary intertwiners for degenerate C*-algebraic universal principal series of SL(n+1) over a local field by explicitely normalizing standard intertwining integrals a…
C*-algebraic intertwiners for principal series: case of SL(2)
Pierre Clare
We construct and normalise intertwining operators at the level of Hilbert modules describing the principal series of SL(2). Normalisation is achieved through the use of a Fourier t…
On the degenerate principal series of complex symplectic groups
Pierre Clare
We apply techniques introduced by Clerc, Kobayashi, Orsted and Pevzner to study the degenerate principal series of Sp(n,C). An explicit description of the K-types is provided and K…
Hilbert modules associated to parabolically induced representations of semisimple Lie groups
Pierre Clare
Given a measured space X with commuting actions of two groups G and H satisfying certain conditions, we construct a Hilbert C*(H)-module E(X) equipped with a left action of C*(G),…