{"paper":{"title":"A multiplicity one theorem for groups of type $A_n$ over discrete valuation rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Pooja Singla, Shiv Prakash Patel","submitted_at":"2018-09-24T03:57:22Z","abstract_excerpt":"Let $\\mathfrak{o}$ be the ring of integers of a non-archimedean local field with the maximal ideal $\\wp$ and the finite residue field of characteristic $p.$ Let $\\mathbf{G}$ be the General Linear or Special Linear group with entries from the finite quotients $\\mathfrak{o}/\\wp^\\ell$ of $\\mathfrak{o}$ and $\\mathbf{U}$ be the subgroup of $\\mathbf{G}$ consisting of upper triangular unipotent matrices. We prove that the induced representation $\\mathrm{Ind}^{\\mathbf{G}}_{\\mathbf{U}}(\\theta)$ of $\\mathbf{G}$ obtained from a ${\\it non-degenerate}$ character $\\theta$ of $\\mathbf{U}$ is multiplicity fre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08743","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":""},"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"}