{"paper":{"title":"Non-admissibility of some universal supersingular representations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Heejong Lee, Nischay Reddy, Ray Li, Vaughan McDonald, Zachary Feng","submitted_at":"2026-05-18T04:18:06Z","abstract_excerpt":"Let $K/\\mathbf{Q}_p$ be an unramified extension of degree $f$ with residue field $k$. Let $\\sigma$ be an irreducible representation of $\\mathrm{GL}_n(k)$ over $\\overline{\\mathbf{F}}_p$. For $n\\ge 3$, we prove that the universal supersingular representation of weight $\\sigma$ is non-admissible and of infinite length when $\\sigma$ is sufficiently generic and satisfies certain technical conditions. This generalizes the previous results for $n=2$ and a non-trivial finite extension $K/\\mathbf{Q}_p$. Our method employs a weight cycling argument together with recent progress on the Serre weight conje"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.17836","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/2605.17836/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"}