The BMM symmetrising trace conjecture for groups $G_4,\,G_5,\,G_6,\,G_7,\,G_8$

Abstract

We prove the BMM symmetrising trace conjecture for the exceptional complex reflection groups $G_4,\,G_5,\,G_6,\,G_7,\,G_8$ 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 generic Hecke algebra associated with each group.