Identities involving (doubly) symmetric polynomials and integrals over Grassmannians
Volume 246 / 2019
Fundamenta Mathematicae 246 (2019), 181-191
MSC: Primary 14M15, 14N15; Secondary 05E05, 55N25.
DOI: 10.4064/fm553-9-2018
Published online: 15 March 2019
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 proof of the Martin formula for the classical Grassmannian.
