What is reference for complex irreducible representations of Hecke algebra of finite Coxeter groups (say generic case q =1)? I am interested in knowing its Wedderburn decomposition. So want explicit information regarding the number of irreducible representations (and parameterization, if any) with their multiplicities. I looked at Kazhdan-Lusztig's paper but not able to get required information.

For example: In case of symmetric group $S_n$, these representations are parametrized by all partitions of $n$ with multiplicities equal to number of standard tableaux.