{"paper":{"title":"Uniqueness of representation--theoretic hyperbolic Kac--Moody groups over $\\Z$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Frank Wagner, Lisa Carbone","submitted_at":"2015-12-15T01:59:17Z","abstract_excerpt":"For a simply laced and hyperbolic Kac--Moody group $G=G(R)$ over a commutative ring $R$ with 1, we consider a map from a finite presentation of $G(R)$ obtained by Allcock and Carbone to a representation--theoretic construction $G^{\\lambda}(R)$ corresponding to an integrable representation $V^{\\lambda}$ with dominant integral weight $\\lambda$. When $R=\\Z$, we prove that this map extends to a group homomorphism $\\rho_{\\lambda,\\Z}: G(\\Z) \\to G^{\\lambda}(\\Z).$ We prove that the kernel $K^{\\lambda}$ of the map $\\rho_{\\lam,\\Z}: G(\\Z)\\to G^{\\lam}(\\Z)$ lies in $H(\\C)$ and if the group homomorphism $\\v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04623","kind":"arxiv","version":2},"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"}