{"paper":{"title":"On the Macdonald correspondence","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Anne-Marie Aubert","submitted_at":"2025-01-04T16:38:24Z","abstract_excerpt":"In 1980 Ian G. Macdonald established an explicit bijection between the isomorphism classes of the irreducible representations of ${\\mathrm{GL}}_n(k)$, where $k$ is a finite field, and inertia equivalence classes of admissible tamely ramified $n$-dimensional Weil-Deligne representations of $W_F$, where $F$ is a non-archimedean local field with residue field $k$ and $W_F$ the absolute Weil group of $F$.\n  We describe a construction of the Macdonald correspondence based on the specialization to ${\\mathrm{GL}}_n(k)$ of Lusztig's classification of irreducible representations of finite groups of Lie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.02332","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/2501.02332/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"}