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

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

2010-09-22

arxiv.org/abs/1009.4285v1

Mathematics

Representation Theory

12 pages, published in the proceedings of FPSAC 2010

Scientific paper

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.

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