  The object of this paper is to prove some general results about rational
idempotents for a finite group $G$ and deduce from them geometric information
about the components that appear in the decomposition of the Jacobian variety
of a curve with $G-$action.
  We give an algorithm to find explicit primitive rational idempotents for any
$G$, as well as for rational projectors invariant under any given subgroup.
These explicit constructions allow geometric descriptions of the factors
appearing in the decomposition of a Jacobian with group action: from them we
deduce the decomposition of any Prym or Jacobian variety of an intermediate
cover, in the case of a Jacobian with $G-$action. In particular, we give a
necessary and sufficient condition for a Prym variety of an intermediate cover
to be such a factor.
