{"paper":{"title":"Explicit Forms of Cluster Variables on Double Bruhat Cells G^{u,e} of type B","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Yuki Kanakubo","submitted_at":"2016-02-27T13:16:48Z","abstract_excerpt":"Let $G$ be a simply connected simple algebraic group over $\\mathbb{C}$ of type $B_r$, $B$ and $B_-$ be its two opposite Borel subgroups, and $W$ be the associated Weyl group. For $u$, $v\\in W$, it is known that the coordinate ring ${\\mathbb C}[G^{u,v}]$ of the double Bruhat cell $G^{u,v}=BuB\\cap B_-vB_-$ is isomorphic to an upper cluster algebra $\\overline{\\mathcal{A}}(\\textbf{i})_{{\\mathbb C}}$ and the generalized minors $\\Delta(k;\\textbf{i})$ are the cluster variables of ${\\mathbb C}[G^{u,v}]$[A.Berenstein, S.Fomin, A.Zelevinsky, Duke Math. J. 126 (2005), 1-52, arxiv:math.RT/0305434]. Recent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08587","kind":"arxiv","version":6},"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"}