{"paper":{"title":"The Combinatorics of $\\mathsf{A_2}$-webs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dongho Moon, Georgia Benkart, Soojin Cho","submitted_at":"2013-12-04T05:05:08Z","abstract_excerpt":"The nonelliptic $\\mathsf{A_2}$-webs with $k$ \"$+$\"s on the top boundary and $3n-2k$ \"$-$\"s on the bottom boundary combinatorially model the space $\\mathsf{Hom}_{\\mathfrak{sl}_3}(\\mathsf{V}^{\\otimes (3n-2k)}, \\mathsf{V}^{\\otimes k})$ of $\\mathfrak{sl}_3$-module maps on tensor powers of the natural $3$-dimensional $\\mathfrak{sl}_3$-module $\\mathsf{V}$, and they have connections with the combinatorics of Springer varieties. Petersen, Pylyavskyy, and Rhodes showed that the set of such $\\mathsf{A_2}$-webs and the set of semistandard tableaux of shape $(3^n)$ and type $\\{1^2,\\dots,k^2,k+1,\\dots, 3n-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1023","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"}