Jun 2014

The local spectrum of the Dirac operator for the universal cover of \$SL_2(\mathbb R)\$

While re-writing our paper “K-theory and limit-of-discrete-series for the universal cover of SL_2(R)” the perspective changed enough to warrant a change of title, and it can now be found on ArXiv at http://arxiv.org/abs/1406.0365 under the name:

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

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.