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

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 $(a_{\lambda \mu }^{\nu }(n,q){)}_{\nu }$ 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.

12 pages, published in the proceedings of FPSAC 2010

References in corpus (1)

• The Hecke algebra and structure constants of the ring of symmetric polynomials