The local spectrum of the Dirac operator for the universal cover of SL_2(R)
The local spectrum of the Dirac operator for the universal cover of SL_2(R)
Using representation theory, we compute the spectrum of the Dirac operator on the universal covering group of SL2(R)SL2(R), exhibiting it as the generator of KK1(C,A)KK1(C,A), where AA is the reduced C?C?-algebra of the group. This yields a new and direct computation of the K -theory of AA. 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.
universal cover of SL2(R), dirac operator, k-theory, dirac cohomology
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
1 February 2016
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 SL_2(R).
Journal of Functional Analysis, 270 (3), .
(doi:10.1016/j.jfa.2015.10.010).
Abstract
Using representation theory, we compute the spectrum of the Dirac operator on the universal covering group of SL2(R)SL2(R), exhibiting it as the generator of KK1(C,A)KK1(C,A), where AA is the reduced C?C?-algebra of the group. This yields a new and direct computation of the K -theory of AA. 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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Dirac_soton_ArXiV.pdf
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The local spectrum of the Dirac operator for the universal cover of SL_2(R).pdf
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1406.0365.pdf
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1-s2.0-S0022123615004322-main.pdf
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Accepted/In Press date: 21 October 2015
e-pub ahead of print date: 28 November 2015
Published date: 1 February 2016
Keywords:
universal cover of SL2(R), dirac operator, k-theory, dirac cohomology
Organisations:
Pure Mathematics
Identifiers
Local EPrints ID: 369701
URI: http://eprints.soton.ac.uk/id/eprint/369701
ISSN: 0022-1236
PURE UUID: e96d0a57-d56f-4efb-8c5f-9c24e46c8bd3
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Date deposited: 13 Oct 2014 10:15
Last modified: 15 Mar 2024 03:22
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