{"paper":{"title":"Unitary representations with Dirac cohomology: finiteness in the real case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Chao-Ping Dong","submitted_at":"2017-08-01T15:14:18Z","abstract_excerpt":"Let $G$ be a complex connected simple algebraic group with a fixed real form $\\sigma$. Let $G(\\mathbb{R})=G^\\sigma$ be the corresponding group of real points. This paper reports a finiteness theorem for the classification of irreducible unitary Harish-Chandra modules of $G(\\mathbb{R})$ (up to equivalence) having non-vanishing Dirac cohomology. Moreover, we study the distribution of the spin norm along Vogan pencils for certain $G(\\mathbb{R})$, with particular attention paid to the unitarily small convex hull introduced by Salamanca-Riba and Vogan."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00383","kind":"arxiv","version":4},"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"}