{"paper":{"title":"The Farahat-Higman ring of wreath products and Hilbert schemes","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.QA","authors_text":"Weiqiang Wang","submitted_at":"2002-05-07T20:14:29Z","abstract_excerpt":"We study the structure constants of the class algebra $R_Z(G_n)$ of the wreath products $G_n$ associated to an arbitrary finite group G with respect to the basis of conjugacy classes. We show that a suitable filtration on $R_Z(G_n)$ gives rise to the graded ring $\\mathcal G_G(n)$ with non-negative integer structure constants independent of n (some of which are computed), which are then encoded in a Farahat-Higman ring $\\mathcal G_G$. The real conjugacy classes of G come to play a distinguished role, and is treated in detail in the case when G is a subgroup of $SL_2(C)$. The above results provi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0205071","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/math/0205071/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"}