{"paper":{"title":"Graded and Geometric Parabolic Induction for Category $\\mathcal{O}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jens Niklas Eberhardt","submitted_at":"2016-03-01T15:48:13Z","abstract_excerpt":"We prove that the parabolic induction functor on BGG-category $\\mathcal{O}$ associated to a complex reductive Lie algebra is gradable, that is, lifts to graded category $\\mathcal{O}$ as constructed by Beilinson-Ginzburg-Soergel. Graded category $\\mathcal{O}$ is equivalent to a category of stratified mixed Tate motives on a corresponding flag variety as recently defined by Soergel-Wendt. The graded version of parabolic induction is induced by a geometric parabolic induction functor we construct on the level of stratified mixed Tate motives. We also describe the effect of parabolic induction on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00327","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"}