{"paper":{"title":"Free Fermionic Schur Functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CO","authors_text":"Slava Naprienko","submitted_at":"2023-01-28T06:45:14Z","abstract_excerpt":"We introduce a new family of Schur functions $s_{\\lambda/\\mu;a,b}(x/y)$ that depend on two sets of variables and two sequences of parameters. These free fermionic Schur functions have a hidden symmetry between the two sets of parameters that allows us to generalize and unify factorial, supersymmetric, and dual Schur functions from literature.\n  We then prove that these functions satisfy the supersymmetric Cauchy identity $$\n  \\sum_{\\lambda}s_{\\lambda;a,b}(x/y)\\widehat{s}_{\\lambda;a,b}(z/w) = \\prod_{i,j}\\frac{1+y_iz_j}{1-x_iz_j}\\frac{1+x_iw_j}{1-y_iw_j}, $$ where $\\widehat{s}_{\\lambda;a,b}(z/w)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.12110","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/2301.12110/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"}