{"paper":{"title":"Hecke algebras for $\\mathrm{GL}_n$ over local fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Valentijn Karemaker","submitted_at":"2015-10-22T12:46:24Z","abstract_excerpt":"We study the local Hecke algebra $\\mathcal{H}_{G}(K)$ for $G = \\mathrm{GL}_n$ and $K$ a non-archimedean local field of characteristic zero. We show that for $G = \\mathrm{GL}_2$ and any two such fields $K$ and $L$, there is a Morita equivalence $\\mathcal{H}_{G}(K) \\sim_M \\mathcal{H}_{G}(L)$, by using the Bernstein decomposition of the Hecke algebra and determining the intertwining algebras that yield the Bernstein blocks up to Morita equivalence. By contrast, we prove that for $G = \\mathrm{GL}_n$, there is an algebra isomorphism $\\mathcal{H}_{G}(K) \\cong \\mathcal{H}_{G}(L)$ which is an isometry"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06606","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":""},"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"}