{"paper":{"title":"Root subsystems of rank 2 hyperbolic root systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GR","math.MP"],"primary_cat":"math-ph","authors_text":"Lisa Carbone, Matt Kownacki, Scott H. Murray, Sowmya Srinivasan","submitted_at":"2015-06-17T18:08:14Z","abstract_excerpt":"Let $\\Delta$ be a rank 2 hyperbolic root system. Then $\\Delta$ has generalized Cartan matrix $H(a,b)= \\left(\\begin{smallmatrix} ~2 & -b\\\\ -a & ~2 \\end{smallmatrix}\\right)$ indexed by $a,b\\in\\mathbb{Z}$ with $ab\\geq 5$. If $a\\neq b$, then $\\Delta$ is non-symmetric and is generated by one long simple root and one short simple root; whereas if $a= b$, $\\Delta$ is symmetric and is generated by two long simple roots. We prove that if $a\\neq b$, then $\\Delta$ contains an infinite family of symmetric rank 2 hyperbolic root subsystems $H(k,k)$ for certain $k\\geq 3$, generated by either two short or tw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05405","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"}