{"paper":{"title":"The regular representations of $\\mathrm{GL}_{N}$ over finite local principal ideal rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alexander Stasinski, Shaun Stevens","submitted_at":"2016-11-15T11:40:05Z","abstract_excerpt":"Let $\\mathfrak{o}$ be the ring of integers in a non-Archimedean local field with finite residue field, $\\mathfrak{p}$ its maximal ideal, and $r\\geq2$ an integer. An irreducible representation of the finite group $G_{r}=\\mathrm{GL}_{N}(\\mathfrak{o}/\\mathfrak{p}^{r})$ is called regular if its restriction to the principal congruence kernel $K^{r-1}=1+\\mathfrak{p}^{r-1}\\mathrm{M}_{N}(\\mathfrak{o}/\\mathfrak{p}^{r})$ consists of representations whose stabilisers modulo $K^{1}$ are centralisers of regular elements in $\\mathrm{M}_{N}(\\mathfrak{o}/\\mathfrak{p})$.\n  The regular representations form the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04796","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"}