{"paper":{"title":"Dirac induction for rational Cherednik algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Dan Ciubotaru, Marcelo De Martino","submitted_at":"2017-10-18T17:54:20Z","abstract_excerpt":"We introduce the local and global indices of Dirac operators for the rational Cherednik algebra $\\mathsf{H}_{t,c}(G,\\mathfrak{h})$, where $G$ is a complex reflection group acting on a finite-dimensional vector space $\\mathfrak{h}$. We investigate precise relations between the (local) Dirac index of a simple module in the category $\\mathcal{O}$ of $\\mathsf{H}_{t,c}(G,\\mathfrak{h})$, the graded $G$-character of the module, the Euler-Poincar\\'e pairing, and the composition series polynomials for standard modules. In the global theory, we introduce integral-reflection modules for $\\mathsf{H}_{t,c}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06847","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"}