Geodesic
Polarizations of Prym varieties for Weyl groups via abelianization
Journal of the European Mathematical Society, Tome 11 (2009) no. 2, pp. 315-349.

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Let π:Z→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 λ consider the curve Y=Z/Stab(λ). The Kanev correspondence defines an abelian subvariety Pλ​ of the Jacobian of Y. We compute the type of the polarization of the restriction of the canonical principal polarization of Jac(Y) to Pλ​ in some cases. In particular, in the case of the group E8​ 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.
DOI : 10.4171/jems/152
Classification : 14-XX, 00-XX
Keywords: Prym variety, principal G-bundle, abelianization, moduli stack 
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     author = {Herbert Lange and Christian Pauly},
     title = {Polarizations of {Prym} varieties for {Weyl} groups via abelianization},
     journal = {Journal of the European Mathematical Society},
     pages = {315--349},
     publisher = {mathdoc},
     volume = {11},
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     year = {2009},
     doi = {10.4171/jems/152},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/152/}
}
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Herbert Lange; Christian Pauly. Polarizations of Prym varieties for Weyl groups via abelianization. Journal of the European Mathematical Society, Tome 11 (2009) no. 2, pp. 315-349. doi : 10.4171/jems/152. http://geodesic.mathdoc.fr/articles/10.4171/jems/152/

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