Centralizers of Iwahori-Hecke algebras

To date, integral bases for the centre of the Iwahori-Hecke algebra of a fi nite Coxeter group have relied on character theoretical results and the iso morphism between the Iwahori-Hecke algebra when semisimple and the group al gebra of the finite Coxeter group. In this paper, we generalize the minimal basis approach of an earlier paper, to provide a way of describing and cal culating elements of the minimal basis for the centre of an Iwahori-Hecke a lgebra which is entirely combinatorial in nature, and independent of both t he above mentioned theories. This opens the door to further generalization of the minimal basis approach to other cases. In particular, we show that generalizing it to centralizer s of parabolic subalgebras requires only certain properties in the Coxeter group. We show here that these properties hold for groups of type A and B, giving us the minimal basis theory for centralizers of any parabolic subalg ebra in these types of Iwahori-Hecke algebra.