Identities involving (doubly) symmetric polynomials and integrals over Grassmannians

Abstract: We obtain identities involving symmetric and doubly symmetric polynomials. These identities provide a way of handling expressions appearing in the Atiyah-Bott-Berline-Vergne formula for Grassmannians. As corollaries, we obtain formulas for integrals over Grassmannians of characteristic classes of the tautological bundles. Moreover, we provide a valid proof of the Martin formula for the classical Grassmannian.