{"paper":{"title":"Products of Geck-Rouquier conjugacy classes and the Hecke algebra of composed permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Pierre-Lo\\\"ic M\\'eliot","submitted_at":"2010-09-22T08:08:30Z","abstract_excerpt":"We show the q-analog of a well-known result of Farahat and Higman: in the center of the Iwahori-Hecke algebra $H_{n,q}$, if $(a_{\\lambda\\mu}^{\\nu}(n,q))_\\nu$ is the set of structure constants involved in the product of two Geck-Rouquier conjugacy classes $\\Gamma_{\\lambda,n}$ and $\\Gamma_{\\mu,n}$, then each coefficient $a_{\\lambda\\mu}^{\\nu}(n,q)$ depends on $n$ and $q$ in a polynomial way. Our proof relies on the construction of a projective limit of the Hecke algebras; this projective limit is inspired by the Ivanov-Kerov algebra of partial permutations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4285","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":""},"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"}