The BMM symmetrising trace conjecture for groups $G_4$, $G_5$, $G_6$, $G_7$, $G_8$
Résumé
We prove the BMM symmetrising trace conjecture for the exceptional irreducible complex reflection groups G4, G 5, G 6, G 7, G 8 using a combination of algorithms programmed in different languages (C++, SAGE, GAP3, Mathematica). Our proof depends on the choice of a suitable basis for the g eneric Hecke algebra associated with each group.