We describe the integral cohomology rings of the flag manifolds of types Bₙ, Dₙ, G₂ and F₄ 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm199-3-5,
author = {Masaki Nakagawa},
title = {A description based on Schubert classes of cohomology of flag manifolds},
journal = {Fundamenta Mathematicae},
volume = {201},
year = {2008},
pages = {273-293},
zbl = {1161.57022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm199-3-5}
}
Masaki Nakagawa. A description based on Schubert classes of cohomology of flag manifolds. Fundamenta Mathematicae, Tome 201 (2008) pp. 273-293. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm199-3-5/