{"paper":{"title":"Cluster monomials in $\\mathbb C[GL_n/N]$, a simplicial fan in the cone of semi-standard Young tableaux, and the Lusztig basis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Gleb Koshevoy","submitted_at":"2014-11-13T14:55:15Z","abstract_excerpt":"We study the cluster monomials and cluster complex in $\\mathbb C[GL_n/N]$. For we consider the {\\em tableau basis} in $\\mathbb C[GL_n/N]$. Namely, an element $\\Delta_T$ of the tableau basis labeled by a semistandard Young tableau $T$ is the product of the flag minors corresponding to columns of $T$. Our main results state: (i) cluster monomials in $\\mathbb C[GL_n/N]$ can be labeled by semistandard Young tableaux such that any cluster monomial has the form $\\Delta_T+$ lexicographically smaller terms; (ii) such labeling distinguish the cluster monomial; (iii) for any seed of the cluster algebra "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3569","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"}