  In this paper we study Prym varieties and their moduli space using the well
known techniques of the infinite Grassmannian. There are three main results of
this paper: a new definition of the BKP hierarchy over an arbitrary base field
(that generalizes the classical one over the complex numbers; a
characterization of Prym varieties in terms of dynamical systems, and explicit
equations for the moduli space of (certain) Prym varieties. For all of these
problems the language of the infinite Grassmannian, in its algebro-geometric
version, allows us to deal with these problems from the same point of view.
