  A new relation between Prym varieties of arbitrary morphisms of algebraic
curves and integrable systems is discovered. The action of maximal commutative
subalgebras of the formal loop algebra of GL(n) defined on certain
infinite-dimensional Grassmannians is studied. It is proved that every
finite-dimensional orbit of the action of traceless elements of these
commutative Lie algebras is isomorphic to the Prym variety associated with a
morphism of algebraic curves. Conversely, it is shown that every Prym variety
can be realized as a finite-dimensional orbit of the action of traceless
diagonal elements of the formal loop algebra, which defines the multicomponent
KP system.
