{"paper":{"title":"Robinson-Schensted-Knuth insertion and characters of symmetric groups and Iwahori-Hecke algebras of type A","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Arun Ram","submitted_at":"1996-07-05T00:00:00Z","abstract_excerpt":"The purpose of this note is to give an insertion scheme proof of the formula, $$p_\\mu = \\sum_{\\lambda\\vdash k} \\chi^\\lambda(\\mu)s_\\lambda,\\formula$$ where $p_\\mu$ is the power sum symmetric function, $s_\\lambda$ is the Schur function and $\\chi^\\lambda(\\mu)$ is the irreducible character of the symmetric group $S_k$ indexed by the partition $\\lambda$ and evaluated at a permutation of cycle type $\\mu=(\\mu_1,\\ldots,\\mu_\\ell)$. The proof of this formula is by direct application of the Robinson-Schensted-Knuth insertion scheme and a recent formula of Roichman."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9607231","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"}