{"paper":{"title":"Representations of reductive groups over finite local rings of length two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Alexander Stasinski, Andrea Vera-Gajardo","submitted_at":"2018-04-13T17:17:46Z","abstract_excerpt":"Let $\\mathbb{F}_{q}$ be a finite field of characteristic $p$, and let $W_{2}(\\mathbb{F}_{q})$ be the ring of Witt vectors of length two over $\\mathbb{F}_{q}$. We prove that for any reductive group scheme $\\mathbb{G}$ over $\\mathbb{Z}$ such that $p$ is very good for $\\mathbb{G}\\times\\mathbb{F}_{q}$, the groups $\\mathbb{G}(\\mathbb{F}_{q}[t]/t^{2})$ and $\\mathbb{G}(W_{2}(\\mathbb{F}_{q}))$ have the same number of irreducible representations of dimension $d$, for each $d$. Equivalently, there exists an isomorphism of group algebras $\\mathbb{C}[\\mathbb{G}(\\mathbb{F}_{q}[t]/t^{2})]\\cong\\mathbb{C}[\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05043","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"}