{"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 $r$. Another result was obtained, which is surprising and co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.4457","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"}