Prym varieties and integrable systems

Given a Galois cover of curves π : X [special characters omitted] Y with any finite Galois group G whose representations are rational, we may consider the Prym variety Prym ρ(X,Y) corresponding to any irreducible representation ρ of G. In chapter two, we will compute the dimension of a Prym variety. In chapter three, we look at the decompositions into Prym varieties of the Jacobians of quotients of X, in the case where G is a Weyl group and the quotient is by a parabolic subgroup P. This corresponds to the decomposition into irreducible representations of the permutation representation [special characters omitted] We look for irreducible components which are common to the permutation representation of all parabolic subgroups of G, and find that for exceptional Weyl groups, there is an “extra” common irreducible component, which does not appear for classical Weyl groups