{"paper":{"title":"The Langlands formula and perverse sheaves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.CT"],"primary_cat":"math.RT","authors_text":"Jiangfan Yuan, Mikhail Kapranov, Olivier Schiffmann, Vadim Schechtman","submitted_at":"2024-12-02T15:49:58Z","abstract_excerpt":"For a complex reductive Lie algebra $\\mathfrak{g}$ with Cartan subalgebra $\\mathfrak{h}$ and Weyl group $W$ we consider the category $\\text{Perv}(W \\backslash \\mathfrak{h})$ of perverse sheaves on $W \\backslash \\mathfrak{h}$ smooth w.r.t. the natural stratification. We construct a category $\\boldsymbol{\\mathcal{C}}$ such that $\\text{Perv}(W\\backslash \\mathfrak{h})$ is identified with the category of functors from $\\boldsymbol{\\mathcal{C}}$ to vector spaces. Objects of $\\boldsymbol{\\mathcal{C}}$ are labelled by standard parabolic subalgebras in $\\mathfrak{g}$. It has morphisms analogous to the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.01638","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.01638/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}