{"paper":{"title":"Simple type theory for metaplectic covers of $\\mathrm{GL}(r)$ over a non-archimedean local field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Jiandi Zou","submitted_at":"2023-08-30T16:57:06Z","abstract_excerpt":"Let $F$ be a non-archimedean locally compact field of residual characteristic $p$, let $G=\\mathrm{GL}_{r}(F)$ and let $\\widetilde{G}$ be an $n$-fold metaplectic cover of $G$ with $\\mathrm{gcd}(n,p)=1$. We study the category $\\mathrm{Rep}_{\\mathfrak{s}}(\\widetilde{G})$ of complex smooth representations of $\\widetilde{G}$ having inertial equivalence class $\\mathfrak{s}=(\\widetilde{M},\\mathcal{O})$, which is a block of the category $\\mathrm{Rep}(\\widetilde{G})$, following the \"type theoretical\" strategy of Bushnell-Kutzko.\n  Precisely, first we construct a \"maximal simple type\" $(\\widetilde{J_{M}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.16143","kind":"arxiv","version":2},"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/2308.16143/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"}