{"paper":{"title":"Plethysms of symmetric functions and representations of $\\mathrm{SL}_2(\\mathbb{C})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Mark Wildon, Rowena Paget","submitted_at":"2019-07-17T16:17:26Z","abstract_excerpt":"Let $\\nabla^\\lambda$ denote the Schur functor labelled by the partition $\\lambda$ and let $E$ be the natural representation of $\\mathrm{SL}_2(\\mathbb{C})$. We make a systematic study of when there is an isomorphism $\\nabla^\\lambda \\!\\mathrm{Sym}^\\ell \\!E \\cong \\nabla^\\mu \\!\\mathrm{Sym}^m \\! E$ of representations of $\\mathrm{SL}_2(\\mathbb{C})$. Generalizing earlier results of King and Manivel, we classify all such isomorphisms when $\\lambda$ and $\\mu$ are conjugate partitions and when one of $\\lambda$ or $\\mu$ is a rectangle. We give a complete classification when $\\lambda$ and $\\mu$ each have "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07616","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"}