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

TL;DR

This paper characterizes the images of Artin groups of types B and D within finite Iwahori-Hecke algebras over finite fields, extending previous results for type A and highlighting parameter dependencies.

Contribution

It generalizes the understanding of Artin group images in Iwahori-Hecke algebras to types B and D over finite fields, considering multi-parameter cases.

Findings

Image depends heavily on parameters in the multi-parameter case

Generalizes earlier work on type A to types B and D

Provides explicit descriptions of the images in the semisimple case

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.