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 Geck–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 Gn, 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 Gn.
Step 2: We choose conjugacy class representatives wC.
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 gw,C.
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. G4, G5, G6, G7, G8, G12, G13, G22.