On the largest representation in type $H_4$

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 $Ω_{48}^+$.

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