Identities involving (doubly) symmetric polynomials and integrals over Grassmannians

Dang Tuan Hiep Fundamenta Mathematicae 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.

Authors

  • Dang Tuan HiepMathematics Division
    National Center for Theoretical Sciences
    No. 1, Sec. 4
    Roosevelt Rd.
    National Taiwan University
    Taipei, 106, Taiwan
    and
    Faculty of Mathematics and Computer Science
    Da Lat University
    No. 1, Phu Dong Thien Vuong Rd., Ward 8
    Da Lat City, Vietnam
    e-mail
    e-mail

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