# On the Connes-Kasparov isomorphism, II: The Vogan classification of essential components in the tempered dual

@inproceedings{Clare2022OnTC, title={On the Connes-Kasparov isomorphism, II: The Vogan classification of essential components in the tempered dual}, author={Pierre Clare and Nigel Higson and Yanli Song}, year={2022} }

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 verification of the Connes-Kasparov conjecture for these groups. These results were originally announced by Antony Wassermann in 1987. In Part I we presented the Morita equivalence and the Connes-Kasparov morphism. In this part we shall compute the morphism using David Vogan’s description of the tempered dual.

## One Citation

### On the Connes-Kasparov isomorphism, I: The reduced C*-algebra of a real reductive group and the K-theory of the tempered dual

- Mathematics
- 2022

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 of the…

## 14 References

### On the Connes-Kasparov isomorphism, I: The reduced C*-algebra of a real reductive group and the K-theory of the tempered dual

- Mathematics
- 2022

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 of the…

### Intertwining operators for semisimple groups, II

- Mathematics
- 1980

The purpose of the present paper is to expand the use of intertwining operators for semisimple Lie groups. In an earlier form (see [20]), these operators were meromorphic continuations of integral…

### On the Classification of Irreducible Representations of Real Algebraic Groups

- Mathematics
- 1988

Suppose G is a connected reductive group over a global field F . Many of the problems of the theory of automorphic forms involve some aspect of study of the representation ρ of G(A(F )) on the space…

### Dirac cohomology of cohomologically induced modules for reductive Lie groups

- Mathematics
- 2015

We extend the setting and a proof of the Vogan's conjecture on Dirac
cohomology to a possibly disconnected real reductive Lie group $G$ in the
Harish-Chandra class. We show that the Dirac cohomology…

### Lie groups beyond an introduction

- Mathematics
- 1988

Preface to the Second Edition Preface to the First Edition List of Figures Prerequisites by Chapter Standard Notation Introduction: Closed Linear Groups Lie Algebras and Lie Groups Complex Semisimple…

### Dirac Operators in Representation Theory

- Mathematics
- 2004

Lie Groups, Lie Algebras and Representations.- Clifford Algebras and Spinors.- Dirac Operators in the Algebraic Setting.- A Generalized Bott-Borel-Weil Theorem.- Cohomological Induction.- Properties…

### Complex Semisimple Lie Algebras

- Mathematics
- 1987

I Nilpotent Lie Algebras and Solvable Lie Algebras.- 1. Lower Central Series.- 2. Definition of Nilpotent Lie Algebras.- 3. An Example of a Nilpotent Algebra.- 4. Engel's Theorems.- 5. Derived…

### Lie groups beyond an introduction, volume 140 of Progress in Mathematics

- 2002