# A geometric construction of the discrete series for semisimple Lie groups

@article{Atiyah1977AGC, title={A geometric construction of the discrete series for semisimple Lie groups}, author={Michael Francis Atiyah and Wilfried Schmid}, journal={Inventiones mathematicae}, year={1977}, volume={42}, pages={1-62} }

## 17 Citations

An index theorem for higher orbital integrals

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Recently, two of the authors of this paper constructed cyclic cocycles on Harish-Chandra's Schwartz algebra of linear reductive Lie groups that detect all information in the $K$-theory of the…

The density theorem for discrete series representations restricted to lattices

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This article considers the relation between the spanning properties of lattice orbits of discrete series representations and the associated lattice co-volume. The focus is on the density theorem,…

An equivariant orbifold index for proper actions

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- 2020

Abstract For a proper, cocompact action by a locally compact group of the form H × G , with H compact, we define an H × G -equivariant index of H -transversally elliptic operators, which takes values…

Dirac Cohomology and Character Lifting

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The endoscopic transfer factor is expressed as difference of characters for the even and odd parts of the spin modules, or Dirac index of the trivial representation. The lifting of tempered…

A K-Theoretic Selberg Trace Formula

- Mathematics
- 2019

Let G be a semisimple Lie group and H a uniform lattice in G. The Selberg trace formula is an equality arising from computing in two different ways the traces of operators on the Hilbert space…

Intégrales orbitales semi-simples et centre de l'algèbre enveloppante

- MathematicsComptes Rendus Mathematique
- 2019

Resume Dans une Note anterieure, le premier auteur a donne une formule locale explicite pour les integrales orbitales semi-simples associees au Casimir. Dans cette Note, nous etendons cette formule a…

On the analogy between real reductive groups and Cartan motion groups: A proof of the Connes-Kasparov isomorphism

- MathematicsJournal of Functional Analysis
- 2019

Abstract Alain Connes and Nigel Higson pointed out in the 1990s that the Connes-Kasparov “conjecture” for the K-theory of reduced group C ⁎ -algebras seemed, in the case of reductive Lie groups, to…

The Baum–Connes conjecture: an extended survey

- MathematicsAdvances in Noncommutative Geometry
- 2019

We present a history of the Baum–Connes conjecture, the methods involved, the current status, and the mathematics it generated.

Twisted Dirac Index and Applications to Characters

- MathematicsSpringer INdAM Series
- 2019

We present recent joint work with Peter Trapa on the notion of twisted Dirac index and its applications to (twisted) characters and to extensions of modules in a short and informal way. We also…