This is the webpage of the project Centers of the Hecke algebra for complex reflection groups. The article of the same name, can be found here.

In this paper we provide a variant of the Geckâ€“Rouquier theorem on the
real case, which also covers the complex case. We also
compute an explicit basis of the center of the Hecke algebra associated
to exceptional groups G_{n},
for n=4,5,6,7,8,12,13,22. In order to do that we
work as follows:

**Step 1:** We find a basis B for the generic Hecke algebra of G_{n}.

**Step 2:** We choose conjugacy class representatives w_{C}.

**Step 3:** We prove that the Hecke algebra is symmetric over its ring of
definition.

**Step 4:** We use the (unique) symmetrising of the Hecke algebra, in order to
find the dual basis of B.

**Step 5:** We use the dual basis and the character table of the Hecke algebra to calculate the coefficients g_{w,C}.

In the following files one can see the particular choices
of Steps 1 and 2 and also the definition of the determinant of the Gram matrix that proves
Step 3: G_{4}, G_{5},
G_{6}, G_{7},
G_{8},
G_{12}, G_{13},
G_{22}.

For Steps 4 and 5 and also for some calculations in Step 1 we use the
following programs in Gap3. We also give a manual
of these programs, where we explain how one can read and use them. In particular, for the group
G_{12} we also include the files with the two counterexamples mentioned in the paper.
G_{4}, G_{5},
G_{6}, G_{7},
G_{8},
G_{12}, G_{13},
G_{22}.