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On the cellular decompositions of the spaces $$G/B$$. (Sur les décompositions 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].

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