Stable Centres of Iwahori-Hecke Algebras of Type A

A celebrated result of Farahat and Higman constructs an algebra FH which "interpolates" the centres Z(ZS(n)) of group algebras of the symmetric groups S-n. We extend these results from symmetric group algebras to type A Iwahori-Hecke algebras, H-n(q). In particular, we explain how to construct an algebra FHq "interpolating" the centres Z(H-n(q)). We prove that FHq is isomorphic to R[q, q(-1)] circle times(Z) Lambda (where R is the ring of integer-valued polynomials, and Lambda is the ring of symmetric functions). The isomorphism can be described as "evaluation at Jucys-Murphy elements", leading to a proof of a conjecture of Francis and Wang. This yields character formulae for the Geck-Rouquier basis of Z(H-n(q)) when acting on Specht modules.