{"paper":{"title":"On rational representations and rational group algebra of $\\operatorname{GL}_2(q)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GR","math.RA"],"primary_cat":"math.RT","authors_text":"Ram Karan Choudhary, Sunil Kumar Prajapati","submitted_at":"2026-06-01T15:57:38Z","abstract_excerpt":"In this article, we study rational representations of $G=\\operatorname{GL}_2(q)$, where $q$ is a prime power. Let $\\rho$ be an irreducible representation of $G$ over $\\mathbb{Q}$. Then $\\rho$ affords the character \\[ \\Omega(\\chi)=m_{\\mathbb{Q}}(\\chi)\\sum_{\\sigma\\in\\operatorname{Gal}(\\mathbb{Q}(\\chi)/\\mathbb{Q})}\\chi^{\\sigma}, \\] for some irreducible complex character $\\chi$ of $G$, where $m_{\\mathbb{Q}}(\\chi)$ denotes the Schur index of $\\chi$ over $\\mathbb{Q}$, with the converse also holding. We obtain a combinatorial description for the counting of inequivalent irreducible $\\mathbb{Q}$-repre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02415","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.02415/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"}