{"paper":{"title":"Conjugate Real Classes in General Linear Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Krishnendu Gongopadhyay, Sudip Mazumder, Sujit Kumar Sardar","submitted_at":"2017-02-27T05:05:50Z","abstract_excerpt":"Let $\\F$ be a field with a non-trivial involution $c: \\alpha \\to \\alpha^c$. An element $g \\in {\\rm GL}_n(\\F)$ is called $c$-real if it is conjugate to $(g^c)^{-1}$. We prove that for $n \\geq 2$, $g \\in {\\rm GL}_n(\\F)$ is $c$-real if and only if it has a representation in some unitary group of degree $n$ over $\\F$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08149","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":""},"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"}