The Chow rings of generalized Grassmannians

Abstract

Based on the Basis theorem of Bruhat--Chevalley [C] and the formula for multiplying Schubert classes obtained in [D\QTR{group}{u}] and programed in [DZ$_{\QTR{group}{1}}$], we introduce a new method computing the Chow rings of flag varieties (resp. the integral cohomology of homogeneous spaces). The method and results of this paper have been extended in [DZ${}_3$, DZ${}_4$] to obtain the integral cohomology rings of all complete flag manifolds, and to construct the integral cohomologies of Lie groups in terms of Schubert classes.

32 pages

References in corpus (2)

• Chow ring structure made simple
• Appendix to "The Chow rings of generalized Grassmannians"

Cited by in corpus (6)

• Schubert calculus and cohomology of Lie groups. Part I. 1-connected Lie groups
• Schubert presentation of the integral cohomology ring of the flag manifolds G/T
• The integral cohomology ring of E_8/T^1E_7
• Homology rigidity of Grassmannians
• The Chow rings of the algebraic groups E_6, E_7, and E_8
• A description based on Schubert classes of cohomology of flag manifolds