A description based on Schubert classes of cohomology of flag manifolds

Volume 199 / 2008

Masaki Nakagawa Fundamenta Mathematicae 199 (2008), 273-293 MSC: Primary 57T15; Secondary 14M15. DOI: 10.4064/fm199-3-5

Abstract

We describe the integral cohomology rings of the flag manifolds of types $B_{n}, D_{n}, G_{2}$ and $F_{4}$ in terms of their Schubert classes. The main tool is the divided difference operators of Bernstein–Gelfand–Gelfand and Demazure. As an application, we compute the Chow rings of the corresponding complex algebraic groups, recovering thereby the results of R. Marlin.

Authors

  • Masaki NakagawaDepartment of General Education
    Takamatsu National College of Technology
    Takamatsu 761-8058, Japan
    e-mail

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