Brodzki, Jacek and Niblo, Graham and Plymen, Roger and Wright, Nick (2013) The spectrum of the Dirac operator for the universal cover of SL_2(R). [MIMS Preprint]
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Abstract
Using representation theory, we compute the spectrum of the Dirac operator on the universal covering group of SL_2(R), exhibiting it as the generator of KK^1(C, A), where A is the reduced C*algebra of the group. This yields a new and direct computation of the Ktheory of A. A fundamental role is played by the limitofdiscreteseries representation, which is the frontier between the discrete and the principal series of the group.
Item Type:  MIMS Preprint 

Uncontrolled Keywords:  Universal cover, Dirac operator, Ktheory 
Subjects:  MSC 2010, the AMS's Mathematics Subject Classification > 19 Ktheory MSC 2010, the AMS's Mathematics Subject Classification > 46 Functional analysis 
Depositing User:  Professor Roger Plymen 
Date Deposited:  16 Apr 2014 
Last Modified:  08 Nov 2017 18:18 
URI:  https://eprints.maths.manchester.ac.uk/id/eprint/2125 
Available Versions of this Item

Ktheory and limitofdiscreteseries for the universal cover of SL_2(R). (deposited 13 Dec 2013)

The Dirac operator and the limitofdiscreteseries for the universal cover of SL_2(R). (deposited 13 Mar 2014)
 The spectrum of the Dirac operator for the universal cover of SL_2(R). (deposited 16 Apr 2014) [Currently Displayed]

The Dirac operator and the limitofdiscreteseries for the universal cover of SL_2(R). (deposited 13 Mar 2014)
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