The spectrum of the Dirac operator for the universal cover of SL_2(R)

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 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.

Item Type:	MIMS Preprint
Uncontrolled Keywords:	Universal cover, Dirac operator, K-theory
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 19 K-theory 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

• K-theory and limit-of-discrete-series for the universal cover of SL_2(R). (deposited 13 Dec 2013)
  • The Dirac operator and the limit-of-discrete-series 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]

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