On the largest representation in type $H_4$

Abstract

In this technical note, we complete the PhD work of A. Esterle about determining the image of any Artin group of finite Coxeter type inside the associated Hecke algebra over a finite field, when the latter is semisimple. The only remaining case was the 48-dimensional irreducible representation in type $H_4$, for which the image is proven here to be $\Omega_{48}^+$.