Prym Subvarieties of Jacobians via Schur correspondances between curves

Abstract

Let $\pi :Z\to X$ be Galois cover of smooth projective curves with Galois group $W$ a Weyl group of a simple Lie group $G$. For a dominant weight $\lambda$, we consider the intermediate curve $Y_λ= Z/\Stab(λ)$. One can realise a Prym variety $P_λ\subset \Jac(Y_λ)$ and we denote ${\phi }_{\lambda }$ the restriction of the principal polarisation of $\Jac(Y_λ)$ upon $P_{\lambda }$. For two dominant weights $\lambda$ and $\mu$, we construct a correspondence ${\Delta }_{\lambda \mu }$ on $Y_{\lambda }\times Y_{\mu }$ and calculate the pull-back of ${\phi }_{\mu }$ by ${\Delta }_{\lambda \mu }$ in terms of ${\phi }_{\lambda }$.

26 pages