Centers of Hecke algebras of complex reflection groups

Abstract

We provide a dual version of the Geck-Rouquier Theorem (Geck and Rouquier in Finite Reductive Groups (Luminy, 1994), Progr. Math., vol. 141, Birkhäuser Boston, Boston, pp. 251–272, 1997) on the center of an Iwahori-Hecke algebra, which also covers the complex case. For the eight complex reflection groups of rank 2, for which the symmetrising trace conjecture is known to be true, we provide a new faithful matrix model for their Hecke algebra H . These models enable concrete calculations inside H . For each of the eight groups, we compute an explicit integral basis of the center of H .