  Let $\pi: Z \ra X$ be a Galois covering of smooth projective curves with
Galois group the Weyl group of a simple and simply-connected Lie group $G$. For
any dominant weight $\lambda$ consider the curve $Y = Z/\Stab(\lambda)$. The
Kanev correspondence defines an abelian subvariety $P_\lambda$ of the Jacobian
of $Y$. We compute the type of the polarization of the restriction of the
canonical principal polarization of $\Jac(Y)$ to $P_\lambda$ in some cases. In
particular, in the case of the group $E_8$ we obtain families of Prym-Tyurin
varieties. The main idea is the use of an abelianization map of the Donagi-Prym
variety to the moduli stack of principal $G$-bundles on the curve $X$.
