{"paper":{"title":"Evaluation of characters of smooth representations of $GL(2,\\mathcal {O})$: I. Strongly primitive representations of even level","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Philippe Roche","submitted_at":"2018-05-03T10:18:22Z","abstract_excerpt":"Let $F$ be a local field, let ${\\mathcal O}$ be its integer ring and $\\varpi$ a uniformizer of its maximal ideal. To an irreducible complex finite dimensional smooth representation $\\pi$ of $GL(2,{\\mathcal O})$ is associated a pair of positive integers $k, k'$ called the level and the sublevel of $\\pi.$ The level is the smallest integer $k$ such that $\\pi$ factorizes through the finite group $GL(2,{\\mathcal O}/\\varpi^k {\\mathcal O})$, whereas the sublevel is the smallest integer $k'\\leq k$ such that there exists $\\chi,$ one dimensional representation of $GL(2,{\\mathcal O}),$ such that $\\pi\\oti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01205","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"}