This is the webpage of the project The BMM Symmetrising Trace Conjecture for Families of Complex Reflection Groups of Rank Two. The article of the same name, can be found here.

In this paper we prove the BMM symmetrising trace conjecture for the exceptional groups of the tetrahedral and octahedral families, namely the groups G_n, for n=4,...15. For this purpose, we work as follows:

Let n ϵ {4, . . . ,15}.

Step 1: We construct a basis B_n for the generic Hecke algebra of G_n and we prove it is actually a basis, by completing the associated coset table.
Step 2: We define the linear map τ_Bn, which takes the value 1 on 1 and 0 on all other elements of the basis.
Step 3: We calculate the Gram matrix A_n:= (τ_Bn (bb')) for all b, b' ϵ B_n
Step 4: We check that A is symmetric, its determinant is a unit and that extra condition for τ that ensures that this is indeed the trace of the BMM conjecture.

In the following files one can find ??????? G₄, G₅, G₆, G₇, G₈, G₉, G₁₀, G₁₁, G₁₂, G₁₃, G₁₄, G₁₅.