zbMATH — the first resource for mathematics

On the cellular decompositions of the spaces \(G/B\). (Sur les d√©compositions cellulaires des espaces \(G/B\).) (French) Zbl 0824.14042
Haboush, William J. (ed.) et al., Algebraic groups and their generalizations: classical methods. Summer Research Institute on algebraic groups and their generalizations, July 6-26, 1991, Pennsylvania State University, University Park, PA, USA. Providence, RI: American Mathematical Society. Proc. Symp. Pure Math. 56, Pt. 1, 1-23 (1994).
This is a fundamental paper on Schubert varieties. The now well-known Bruhat order (rather Bruhat-Chevalley order) on the Weyl group goes back to this paper. The author also proves that the classes of Schubert varieties form a \(\mathbb{Z}\)-basis for the Chow group of the flag variety. The author also computes the product \(X \cdot Y\), where \(X\) is the class of a Schubert variety, and \(Y\) that of a Schubert divisor.
This paper is indispensable in the theory of Schubert varieties.
For the entire collection see [Zbl 0793.00018].

14M15 Grassmannians, Schubert varieties, flag manifolds
14C05 Parametrization (Chow and Hilbert schemes)
14M17 Homogeneous spaces and generalizations
14C15 (Equivariant) Chow groups and rings; motives
PDF BibTeX Cite