{"paper":{"title":"A new generalization of Hermite's reciprocity law","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Daniel Penazzi, Leandro Cagliero","submitted_at":"2015-10-06T16:44:10Z","abstract_excerpt":"Given a partition $\\lambda$ of $n$, the {\\it Schur functor} $\\mathbb{S}_\\lambda$ associates to any complex vector space $V$, a subspace $\\mathbb{S}_\\lambda(V)$ of $V^{\\otimes n}$. Hermite's reciprocity law, in terms of the Schur functor, states that $\n  \\mathbb{S}_{(p)}\\left(\\mathbb{S}_{(q)}(\\mathbb{C}^2)\\right)\\simeq \\mathbb{S}_{(q)}\\left(\\mathbb{S}_{(p)}(\\mathbb{C}^2)\\right). $\nWe extend this identity to many other identities of the type $\\mathbb{S}_{\\lambda}\\left(\\mathbb{S}_{\\delta}(\\mathbb{C}^2)\\right)\\simeq \\mathbb{S}_{\\mu}\\left(\\mathbb{S}_{\\epsilon}(\\mathbb{C}^2)\\right)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01657","kind":"arxiv","version":1},"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"}