  Given a tame Galois branched cover of curves pi: X -> Y with any finite
Galois group G whose representations are rational, we compute the dimension of
the (generalized) Prym variety corresponding to any irreducible representation
\rho of G. This formula can be applied to the study of algebraic integrable
systems using Lax pairs, in particular systems associated with Seiberg-Witten
theory. However, the formula is much more general and its computation and proof
are entirely algebraic.
