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We call these invariant factors Cartan invariants.\n  In a previous paper, the second author calculated these Cartan invariants when $\\ell=p^r$, $p$ prime, and $r\\leq p$ and went on to conjecture that the formulae should hold for all $r$. Another result was obtained, which is surprising and co"},"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":"0809.4457","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2008-09-25T17:13:47Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"8106d5278ec58f998a0414eba0383266af813aa983eb12aabc02d959156218f0","abstract_canon_sha256":"01729cdba794b78a84738f0e6f322f953185e671a4fe54d6470058e95aef0854"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:11.148917Z","signature_b64":"mKhPoQY6F71p2ZDPaGrzNvoTqqHnrx5TWQEW27CJdMUp7fhrKEF/PF1wbfp202uEIc0Z9J4ikjmJcwd42bq7BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6e002703eba37501a6949ea8d2aab493350975f910fc2f82af194a8c4e18fc4","last_reissued_at":"2026-05-18T02:58:11.148214Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:11.148214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cartan Invariants of Symmetric Groups and Iwahori-Hecke Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Christine Bessenrodt, David Hill","submitted_at":"2008-09-25T17:13:47Z","abstract_excerpt":"K\\\"{u}lshammer, Olsson and Robinson conjectured that a certain set of numbers determined the invariant factors of the $\\ell$-Cartan matrix for $S_n$ (equivalently, the invariant factors of the Cartan matrix for the Iwahori-Hecke algebra $\\mathcal{H}_n(q)$, where $q$ is a primitive $\\ell$th root of unity). We call these invariant factors Cartan invariants.\n  In a previous paper, the second author calculated these Cartan invariants when $\\ell=p^r$, $p$ prime, and $r\\leq p$ and went on to conjecture that the formulae should hold for all $r$. 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