{"paper":{"title":"Jack polynomials and Hilbert schemes of points on surfaces","license":"","headline":"","cross_cats":["hep-th","math.AG","math.QA","nlin.SI","q-alg","solv-int"],"primary_cat":"alg-geom","authors_text":"Hiraku Nakajima","submitted_at":"1996-10-31T11:25:57Z","abstract_excerpt":"The Jack symmetric polynomials $P_\\lambda^{(\\alpha)}$ form a class of symmetric polynomials which are indexed by a partition $\\lambda$ and depend rationally on a parameter $\\alpha$. They reduced to the Schur polynomials when $\\alpha=1$, and to other classical families of symmetric polynomials for several specific parameters.\n  It is well-known that Schur polynomials can be realized as certain elements of homology groups of Grassmann manifolds. The purpose of this paper is to give a similar geometric realization for Jack polynomials. However, spaces which we use are totally different. Our space"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9610021","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/alg-geom/9610021/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"}