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The local spectrum of the Dirac operator for the universal cover of SL2(R)

The local spectrum of the Dirac operator for the universal cover of SL2(R)
The local spectrum of the Dirac operator for the universal cover of SL2(R)
Using representation theory, we compute the spectrum of the Dirac operator on the universal covering group of SL2(R), exhibiting it as the generator of KK1(C,A), where A is the reduced C*-algebra of the group. This yields a new and direct computation of the K-theory of A. A fundamental role is played by the limit-of-discrete-series representation, which is the frontier between the discrete and the principal series of the group. We provide a detailed analysis of the localised spectra of the Dirac operator and compute the Dirac cohomology.
0022-1236
957-975
Brodzki, Jacek
b1fe25fd-5451-4fd0-b24b-c59b75710543
Niblo, Graham A.
43fe9561-c483-4cdf-bee5-0de388b78944
Plymen, Roger
76de3dd0-ddcb-4a34-98e1-257dddb731f5
Wright, Nick
f4685b8d-7496-47dc-95f0-aba3f70fbccd
Brodzki, Jacek
b1fe25fd-5451-4fd0-b24b-c59b75710543
Niblo, Graham A.
43fe9561-c483-4cdf-bee5-0de388b78944
Plymen, Roger
76de3dd0-ddcb-4a34-98e1-257dddb731f5
Wright, Nick
f4685b8d-7496-47dc-95f0-aba3f70fbccd

Brodzki, Jacek, Niblo, Graham A., Plymen, Roger and Wright, Nick (2016) The local spectrum of the Dirac operator for the universal cover of SL2(R). Journal of Functional Analysis, 270 (3), Winter Issue, 957-975. (doi:10.1016/j.jfa.2015.10.010).

Record type: Article

Abstract

Using representation theory, we compute the spectrum of the Dirac operator on the universal covering group of SL2(R), exhibiting it as the generator of KK1(C,A), where A is the reduced C*-algebra of the group. This yields a new and direct computation of the K-theory of A. A fundamental role is played by the limit-of-discrete-series representation, which is the frontier between the discrete and the principal series of the group. We provide a detailed analysis of the localised spectra of the Dirac operator and compute the Dirac cohomology.

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More information

Accepted/In Press date: 21 October 2015
e-pub ahead of print date: 28 November 2015
Published date: 1 February 2016
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 373669
URI: https://eprints.soton.ac.uk/id/eprint/373669
ISSN: 0022-1236
PURE UUID: 2281216d-89f8-406b-b1f6-732516521795
ORCID for Nick Wright: ORCID iD orcid.org/0000-0003-4884-2576

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Date deposited: 28 Jan 2015 10:56
Last modified: 25 May 2019 00:34

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