{"paper":{"title":"Fermionic representation for basic hypergeometric functions related to Schur polynomials","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"A.Yu.Orlov, D.M.Scherbin","submitted_at":"2000-01-06T22:32:36Z","abstract_excerpt":"We present the fermionic representation for the q-deformed hypergeometric functions related to Schur polynomials considered by S.Milne \\cite{Milne}. For $q=1$ these functions are also known as hypergeometric functions of matrix argument which are related to zonal spherical polynomials for $GL(N,C)/U(N)$ symmetric space. We show that these multivariable hypergeometric functions are tau-functions of the KP hierarchy. At the same time they are the ratios of Toda lattice tau-functions considered by Takasaki in \\cite{Tinit}, \\cite{T} evaluated at certain values of higher Toda lattice times. The var"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0001001","kind":"arxiv","version":4},"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/nlin/0001001/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"}