{"paper":{"title":"The local spectrum of the Dirac operator for the universal cover of $SL_2(\\mathbb R)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.OA","math.SP"],"primary_cat":"math.RT","authors_text":"Graham A. Niblo, Jacek Brodzki, Nick Wright, Roger Plymen","submitted_at":"2014-06-02T13:40:52Z","abstract_excerpt":"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 cohomo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0365","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}