{"paper":{"title":"Calculations with graded perverse-coherent sheaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Pramod N. Achar, William D. Hardesty","submitted_at":"2018-06-20T15:04:03Z","abstract_excerpt":"In this paper, we carry out several computations involving graded (or $\\mathbb{G}_{\\mathrm{m}}$-equivariant) perverse-coherent sheaves on the nilpotent cone of a reductive group in good characteristic. In the first part of the paper, we compute the weight of the $\\mathbb{G}_{\\mathrm{m}}$-action on certain normalized (or \"canonical\") simple objects, confirming an old prediction of Ostrik. In the second part of the paper, we explicitly describe all simple perverse coherent sheaves for $G = PGL_3$, in every characteristic other than 2 or 3. Applications include an explicit description of the coho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07780","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"}