{"paper":{"title":"The Robinson-Schensted Correspondence and $A_2$-web Bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GT"],"primary_cat":"math.RT","authors_text":"Heather Russell, Julianna Tymoczko, Matthew Housley","submitted_at":"2013-07-24T16:50:20Z","abstract_excerpt":"We study natural bases for two constructions of the irreducible representation of the symmetric group corresponding to $[n,n,n]$: the {\\em reduced web} basis associated to Kuperberg's combinatorial description of the spider category; and the {\\em left cell basis} for the left cell construction of Kazhdan and Lusztig. In the case of $[n,n]$, the spider category is the Temperley-Lieb category; reduced webs correspond to planar matchings, which are equivalent to left cell bases. This paper compares the images of these bases under classical maps: the {\\em Robinson-Schensted algorithm} between perm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6487","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"}