  We introduce polynomials that represent general degeneracy loci for maps of
vector bundles. These polynomials specialize to the known classical and quantum
forms of single and double Schubert polynomials. This is the final version of
the paper, to appear in Duke Math. J. The results are strengthened because
Lakshmibai and Magyar have proved a conjecture from the previous version: in
the universal case, these loci are Cohen-Macaulay.
