Abstract
Based on the basis theorem of Bruhat–Chevalley (in Algebraic Groups and Their Generalizations: Classical Methods, Proceedings of Symposia in Pure Mathematics, vol. 56 (part 1), pp. 1–26, AMS, Providence, 1994) and the formula for multiplying Schubert classes obtained in (Duan, Invent. Math. 159:407–436, 2005) and programmed in (Duan and Zhao, Int. J. Algebra Comput. 16:1197–1210, 2006), we introduce a new method for 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 (Duan and Zhao, arXiv:math.AT/0801.2444 and arXiv:math.AT/0711.2541) 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.
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