{"paper":{"title":"Structure of Hecke algebras arising from types","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Jeffrey D. Adler, Jessica Fintzen, Kazuma Ohara, Manish Mishra","submitted_at":"2024-08-14T20:23:09Z","abstract_excerpt":"Let $G$ denote a connected reductive group over a nonarchimedean local field $F$ of residue characteristic $p$, and let $\\mathcal{C}$ denote an algebraically closed field of characteristic $\\ell \\neq p$. If $\\rho$ is an irreducible, smooth $\\mathcal{C}$-representation of a compact, open subgroup $K$ of $G(F)$, then the pair $(K,\\rho)$ gives rise to a Hecke algebra $\\mathcal{H}(G(F),(K, \\rho))$. For a large class of pairs $(K,\\rho)$, we show that $\\mathcal{H}(G(F),(K, \\rho))$ is a semi-direct product of an affine Hecke algebra with explicit parameters with a twisted group algebra, and that it i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.07801","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/2408.07801/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"}