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

Christina Boura (1, 2) , Eirini Chavli (3) , Maria Chlouveraki (1) , Konstantinos Karvounis (4)

1 LMV - Laboratoire de Mathématiques de Versailles
2 COSMIQ - Cryptologie symétrique, cryptologie fondée sur les codes et information quantique
3 Universität Stuttgart [Stuttgart]
4 Institut für Mathematik [Zürich]

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.

Domains: Mathematics [math]

Christina Boura, Eirini Chavli, Maria Chlouveraki, Konstantinos Karvounis. The BMM symmetrising trace conjecture for groups $G_4$, $G_5$, $G_6$, $G_7$, $G_8$. Journal of Symbolic Computation, 2020, 96, pp.62-84. ⟨10.1016/j.jsc.2019.02.012⟩. ⟨hal-02147376⟩