{"paper":{"title":"Local Representations of the Flat Virtual Braid Group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Malak M. Dally, Mohamad N. Nasser, Mohammad Y. Chreif","submitted_at":"2025-03-09T13:22:42Z","abstract_excerpt":"We prove that any complex local representation of the flat virtual braid group, $FVB_2$, into $GL_2(\\mathbb{C})$, has one of the types $\\lambda_i: FVB_2 \\rightarrow GL_2(\\mathbb{C})$, $1\\leq i\\leq 12$. We find necessary and sufficient conditions that guarantee the irreducibility of representations of type $\\lambda_i$, $1\\leq i\\leq 5$, and we prove that representations of type $\\lambda_i$, $6\\leq i\\leq 12$, are reducible. Regarding faithfulness, we find necessary and sufficient conditions for representations of type $\\lambda_6$ or $\\lambda_7$ to be faithful. Moreover, we give sufficient conditi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.06607","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"}