{"paper":{"title":"Path model for an extremal weight module over the quantized hyperbolic Kac-Moody algebra of rank 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Daisuke Sagaki, Dongxiao Yu","submitted_at":"2017-12-04T11:15:29Z","abstract_excerpt":"Let $\\mathfrak{g}$ be a hyperbolic Kac-Moody algebra of rank 2, and set $\\lambda=\\Lambda_{1} - \\Lambda_{2}$, where $\\Lambda_{1}$, $\\Lambda_{2}$ are the fundamental weights. Denote by $V(\\lambda)$ the extremal weight module of extremal weight $\\lambda$ with $v_\\lambda$ the extremal weight vector, and by $\\mathcal{B}(\\lambda)$ the crystal basis of $V(\\lambda)$ with $u_\\lambda$ the element corresponding to $v_\\lambda$. We prove that (i) $\\mathcal{B}(\\lambda)$ is connected, (ii) the subset $\\mathcal{B}(\\lambda)_{\\mu}$ of elements of weight $\\mu$ in $\\mathcal{B}(\\lambda)$ is a finite set for every "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.01009","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"}