Cauchy identities for universal Schubert polynomials

We prove the Cauchy type identities for the universal double Schubert polynomials, introduced recently by W. Fulton. As a corollary, the determinantal formula for some specializations of the universal double Schubert polynomials corresponding to the Grassmannian permutations are obtained. We also introduce and study the universal Schur functions and multiparameter deformation of Schubert polynomials.