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

Autor:	Brodzki, Jacek, Niblo, Graham A., Plymen, Roger, Wright, Nick
Rok vydání:	2014
Předmět:	Mathematics - Representation Theory Mathematics - K-Theory and Homology Mathematics - Operator Algebras Mathematics - Spectral Theory 06B15 22E45 46L80
Druh dokumentu:	Working Paper
Popis:	Using representation theory, we compute the spectrum of the Dirac operator on the universal covering group of $SL_2(\mathbb R)$, exhibiting it as the generator of $KK^1(\mathbb C, \mathfrak A)$, where $\mathfrak A$ is the reduced $C^*$-algebra of the group. This yields a new and direct computation of the $K$-theory of $\mathfrak A$. 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. Comment: 17 pages, 6 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1406.0365 Zobrazit plný text záznamu View this record from Arxiv