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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1804.05043","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-04-13T17:17:46Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"44fb5c5dba72a7e4187dc99d95414a891d9160e9b5c235f93d694e253ceeb011","abstract_canon_sha256":"d249adc3d7a856a0f6da7a23215ce5c10f4533788a94218ce9f8db78e983e2c2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:44.192984Z","signature_b64":"90Nnn2wiRteHzbfW5UM0LCQ27itn684BnUjGCZiYd/PspUnw8yaPaSe/4FwqD0FRC5cpGT+DjJ2jWMSMmXEhCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aeed1c7104feb58c2ce81e68f16433e18df00597d9219601014aeff610e0bc58","last_reissued_at":"2026-05-17T23:53:44.192425Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:44.192425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $d$. 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