The BMM symmetrising trace conjecture for groups G_4, C_5, G_6, G_7, G_8

摘要

We prove the BMM symmetrising trace conjecture for the exceptional irreducible 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. (C) 2019 Elsevier Ltd. All rights reserved.