  In this doctoral thesis, we will determine the image of Artin groups
associated to all finite irreducible Coxeter groups inside their associated
finite Iwahori-Hecke algebra. This was done in type $A$ by Brunat, Magaard and
Marin. The Zariski closure of the image was determined in the generic case by
Marin. It is suggested by strong approximation that the results should be
similar in the finite case. However, the conditions required to use are much
too strong and would only provide a portion of the results. We show in this
thesis that they are but that new phenomena arise from the different field
factorizations. The techniques used in the finite case are very different from
the ones in the generic case. The main arguments come from finite group theory.
In high dimension, we will use a theorem by Guralnick-Saxl which uses the
classification of finite simple groups to give a condition for subgroups of
linear groups to be classical groups in a natural representation. In low
dimension, we will mainly use the classification of maximal subgroups of
classical groups determined by Bray, Holt and Roney-Dougal for the complicated
cases.
  We find some new $W$-graphs in types $H_4$, $E_6$ and $E_8$ which provide
different information from the usual ones. They are all associated in a natural
way to a bilinear form which is very complicated to obtain in the previous
models. In this model, the bilinear form is obtained using only the
two-colorability and its matrix in a well chosen basis is anti-diagonal. The
uniqueness properties can probably be extended in a more general setting and
understanding which setting this is may be worth considering.
