  Let X be the flag variety of the symplectic group. We propose a theory of
combinatorially explicit Schubert polynomials which represent the Schubert
classes in the Borel presentation of the cohomology ring of X. We use these
polynomials to describe the arithmetic Schubert calculus on X. Moreover, we
give a method to compute the natural arithmetic Chern numbers on X, and show
that they are all rational numbers.
