Geodesic
Schubert cells and cohomology of the spaces $G/P$
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 28 (1973) no. 3, pp. 1-26

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We study the homological properties of the factor space $G/P$, where $G$ is a complex semisimple Lie group and $P$ a parabolic subgroup of $G$. To this end we compare two descriptions of the cohomology of such spaces. One of these makes use of the partition of $G/P$ into cells (Schubert cells), while the other consists in identifying the cohomology of $G/P$ with certain polynomials on the Lie algebra of the Cartan subgroup $H$ of $G$. The results obtained are used to describe the algebraic action of the Weyl group $W$ of $G$ on the cohomology of $G/P$. 
@article{RM_1973_28_3_a0,
     author = {J. H. Bernstein and I. M. Gel'fand and S. I. Gel'fand},
     title = {Schubert cells and cohomology of the spaces $G/P$},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {1--26},
     publisher = {mathdoc},
     volume = {28},
     number = {3},
     year = {1973},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_1973_28_3_a0/}
}
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J. H. Bernstein; I. M. Gel'fand; S. I. Gel'fand. Schubert cells and cohomology of the spaces $G/P$. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 28 (1973) no. 3, pp. 1-26. http://geodesic.mathdoc.fr/item/RM_1973_28_3_a0/