{"paper":{"title":"$\\mathrm{PGL}_n(\\mathbb{C})$-character stacks and Langlands duality over finite fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Emmanuel Letellier, Tommaso Scognamiglio","submitted_at":"2024-12-04T11:35:39Z","abstract_excerpt":"In this paper we study the mixed Poincar\\'e polynomial of generic $\\mathrm{PGL}_n(\\mathbb{C})$-character stacks with coefficients in some local systems arising from the conjugacy classes of $\\mathrm{PGL}_n(\\mathbb{C})$ which have non-connected stabiliser. We give a conjectural formula that we prove to be true under the Euler specialisation. We then prove that this conjectured formula interpolates the structure coefficients of the two based rings$ \\left(\\mathcal{C}(\\mathrm{PGL}_n(\\mathbb{F}_q)),Loc(\\mathrm{PGL}_n),*\\right)$ and $\\left(\\mathcal{C}(\\mathrm{SL}_n(\\mathbb{F}_q)), CS(\\mathrm{SL}_n),"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.03234","kind":"arxiv","version":6},"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/2412.03234/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"}