{"paper":{"title":"Skew Howe duality and random rectangular Young tableaux","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Greta Panova, Piotr \\'Sniady","submitted_at":"2017-05-22T08:22:39Z","abstract_excerpt":"We consider the decomposition into irreducible components of the external power $\\Lambda^p(\\mathbb{C}^m\\otimes \\mathbb{C}^n)$ regarded as a $\\operatorname{GL}_m\\times\\operatorname{GL}_n$-module. Skew Howe duality implies that the Young diagrams from each pair $(\\lambda,\\mu)$ which contributes to this decomposition turn out to be conjugate to each other, i.e.~$\\mu=\\lambda'$. We show that the Young diagram $\\lambda$ which corresponds to a randomly selected irreducible component $(\\lambda,\\lambda')$ has the same distribution as the Young diagram which consists of the boxes with entries $\\leq p$ o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07604","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"}