{"paper":{"title":"On character tables for fusion systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jason Semeraro, Thomas Lawrence","submitted_at":"2025-10-10T11:20:07Z","abstract_excerpt":"A character table $X$ for a saturated fusion system $\\mathcal{F}$ on a finite $p$-group $S$ is the square matrix of values associated to a basis of the lattice of virtual $\\mathcal{F}$-stable ordinary characters of $S$. We investigate a conjecture of the second author which equates the determinant of $X \\overline{X}$ (the square of the volume of this lattice) with the product of the orders of $S$-centralisers of fully $\\mathcal{F}$-centralised $\\mathcal{F}$-class representatives. This statement is exactly column orthogonality for the character table of $S$ when $\\mathcal{F}=\\mathcal{F}_S(S)$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.09277","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.09277/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}