{"paper":{"title":"Some Singular Vector-valued Jack and Macdonald Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Charles F. Dunkl","submitted_at":"2019-02-06T18:07:38Z","abstract_excerpt":"For each partition $\\tau$ of $N$ there are irreducible modules of the symmetric groups $\\mathcal{S}_{N}$ or the corresponding Hecke algebra $\\mathcal{H}_{N}\\left( t\\right) $ whose bases consist of reverse standard Young tableaux of shape $\\tau$. There are associated spaces of nonsymmetric Jack and Macdonald polynomials taking values in these modules, respectively.The Jack polynomials are a special case of those constructed by Griffeth for the infinite family $G\\left( n,p,N\\right) $ of complex reflection groups. The Macdonald polynomials were constructed by Luque and the author. For both the gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02310","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"}