Lax equations, weight lattices, and Prym-Tjurin varieties (Q1282111)

The authors discuss relation between two approaches to integrable systems -- by Lie algebras and by algebraic curves. It is shown that the line bundles on the algebraic curves giving the evolution of the system are pullbacks of the line bundles of the Borel-Weil theory. A Weyl group action on the Jacobian of the master spectral curve picks out a sub-abelian variety.