The Dirac operator and the limit-of-discrete-series for the universal cover of SL_2(R)

Brodzki, Jacek and Niblo, Graham and Plymen, Roger and Wright, Nick (2013) The Dirac operator and the limit-of-discrete-series for the universal cover of SL_2(R). [MIMS Preprint]

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Abstract

The principal series of the universal cover of $SL_2(R)$ admits a limit-of-discrete-series. Starting with this representation, we construct certain spinor fields on which the Dirac operator $D$ is a multiplication operator. This creates an unbounded Kasparov triple which generates $K_1$ of the reduced C*-algebra.

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:	13 Mar 2014
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/2113

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

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