Image of the Artin groups of classical types inside the finite Iwahori–Hecke algebras

Abstract

We determine the image of the Artin groups of types B and D inside the Iwahori–Hecke algebras, when defined over finite fields, in the semisimple case. This generalizes earlier work on type A by Brunat, Magaard and Marin. In this multi-parameter case, this image depends heavily on the parameters.