Identities involving (doubly) symmetric polynomials and integrals over Grassmannians
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 proof of the Martin formula for the classical Grassmannian.