Abstract
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.
Original language | Russian |
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Pages (from-to) | 3-26 |
Number of pages | 24 |
Journal | Uspekhi Matematicheskikh Nauk |
Volume | 28 |
Issue number | 3(171) |
DOIs | |
State | Published - 1973 |
Externally published | Yes |