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The dirac operator and the principal series for complex semisimple lie groups

The dirac operator and the principal series for complex semisimple lie groups
The dirac operator and the principal series for complex semisimple lie groups

The Dirac operator plays a fundamental role in the geometric construction of the discrete series for semisimple Lie groups. We show that, at the level of K-theory, the Dirac operator also plays a central role in connection with the principal series for complex connected semisimple Lie groups. This proves the Connes-Kasparov conjecture for such groups.

0022-1236
269-286
Penington, M. G.
db035151-554d-4ed3-8dfd-d6f445847c1e
Plymen, R. J.
76de3dd0-ddcb-4a34-98e1-257dddb731f5
Penington, M. G.
db035151-554d-4ed3-8dfd-d6f445847c1e
Plymen, R. J.
76de3dd0-ddcb-4a34-98e1-257dddb731f5

Penington, M. G. and Plymen, R. J. (1983) The dirac operator and the principal series for complex semisimple lie groups. Journal of Functional Analysis, 53 (3), 269-286. (doi:10.1016/0022-1236(83)90035-6).

Record type: Article

Abstract

The Dirac operator plays a fundamental role in the geometric construction of the discrete series for semisimple Lie groups. We show that, at the level of K-theory, the Dirac operator also plays a central role in connection with the principal series for complex connected semisimple Lie groups. This proves the Connes-Kasparov conjecture for such groups.

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Published date: 1 October 1983

Identifiers

Local EPrints ID: 422329
URI: https://eprints.soton.ac.uk/id/eprint/422329
ISSN: 0022-1236
PURE UUID: af931be5-f139-4be4-9ce8-110bf30de669

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Date deposited: 20 Jul 2018 16:31
Last modified: 20 Jul 2018 16:31

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Contributors

Author: M. G. Penington
Author: R. J. Plymen

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