{"paper":{"title":"Universal symplectic/orthogonal functions and general branching rules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.CO","authors_text":"Danxia Wang, Naihuan Jing, Zhihong Jin, Zhijun Li","submitted_at":"2022-09-02T00:38:14Z","abstract_excerpt":"In this paper, we first introduce a family of universal symplectic functions $sp_\\lambda(\\mathbf{x}^{\\pm};\\mathbf{z})$ that include symplectic Schur functions $sp_\\lambda(\\mathbf{x}^{\\pm})$, odd symplectic characters $sp_\\lambda(\\mathbf{x}^{\\pm};z)$, universal symplectic characters $sp_\\lambda(\\mathbf{z})$ and intermediate symplectic characters as subfamilies. We then realize the universal symplectic functions by vertex operators, which naturally lead to their skew versions, and show that $sp_\\lambda(\\mathbf{x}^{\\pm};\\mathbf{z})$ obey the general branching rules. This also gives the Gelfand-Ts"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.00767","kind":"arxiv","version":3},"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/2209.00767/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"}