{"paper":{"title":"Geometric representations of graded and rational Cherednik algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alexei Oblomkov, Zhiwei Yun","submitted_at":"2014-07-21T22:53:06Z","abstract_excerpt":"We provide geometric constructions of modules over the graded Cherednik algebra $\\mathfrak{H}^{gr}_\\nu$ and the rational Cherednik algebra $\\mathfrak{H}^{rat}_\\nu$ attached to a simple algebraic group $\\mathbb{G}$ together with a pinned automorphism $\\theta$. These modules are realized on the cohomology of affine Springer fibers (of finite type) that admit $\\mathbb{C}^*$-actions. In the rational Cherednik algebra case, the standard grading on these modules is derived from the perverse filtration on the cohomology of affine Springer fibers coming from its global analog: Hitchin fibers. When $\\t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5685","kind":"arxiv","version":2},"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"}