{"paper":{"title":"The support of Kostant's weight multiplicity formula is an order ideal in the weak Bruhat order","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Alexander N. Wilson, Esther Banaian, Kimberly J. Harry, Kimberly P. Hadaway, Melanie J. Ferreri, Nicholas Mayers, Owen C. Goff, Pamela E. Harris, Portia X. Anderson, Shiyun Wang","submitted_at":"2024-12-22T01:46:30Z","abstract_excerpt":"For integral weights $\\lambda$ and $\\mu$ of a classical simple Lie algebra $\\mathfrak{g}$, Kostant's weight multiplicity formula gives the multiplicity of the weight $\\mu$ in the irreducible representation with highest weight $\\lambda$, which we denote by $m(\\lambda,\\mu)$. Kostant's weight multiplicity formula is an alternating sum over the Weyl group of the Lie algebra whose terms are determined via a vector partition function. The Weyl alternation set $\\mathcal{A}(\\lambda,\\mu)$ is the set of elements of the Weyl group that contribute nontrivially to the multiplicity $m(\\lambda,\\mu)$. In this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.16820","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.16820/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}