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On the action of Hecke algebras on the Specht modules

The Hecke algebras associated with the Young subgroups of S n acts on the corresponding Specht module by scalars given by Green character. This partially (and in some cases completely) characterizes the Specht module as being eigenvectors for the elements of the Hecke algebra with eigenvalues given by the values of Green character. We define an equivalence relation which simplifies the problem of calculating the values of such character and reduce it to a combinatorial one. We also determine the values of that character in the case of two parts partition of n.