Products of Geck-Rouquier conjugacy classes and the Hecke algebra of composed permutations

2010/09/22 by Pierre‐Loïc Méliot, Méliot, Pierre-Loïc · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1009.4285

Abstract

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_λμ^ν(n,q))_ν is the set of structure constants involved in the product of two Geck-Rouquier conjugacy classes Γ_λ,n and Γ_μ,n, then each coefficient a_λμ^ν(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.

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