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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1705.07604","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-22T08:22:39Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"abc549f15bbf7da2108a34ceb4349de2290d65ef41ff88f41f3369eeda94bb1f","abstract_canon_sha256":"56a927cfc60e62862ed2d31734201dd6be950c7fce0ddf21bdf14b01d62e0a60"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:01.753268Z","signature_b64":"f7F9CpDNlJ387rNWne+xNH5Szyzy6+v3s5v6Wmpe7BYF1odBueq2deSy8+JacsK+4HFvcyzSXz54sPQNfpkbAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ddb44f9bc93cb7e1c60cb184bf58c05185e0ce1e3e832e71604e6773eef90158","last_reissued_at":"2026-05-18T00:25:01.752844Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:01.752844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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