Schubert cells, and the cohomology of the spaces G/P: КЛЕТКИ ШУБЕРТА И КОГОМОЛОГИИ ПРОСТРАНСТВ О/Р

I. N. Bernštein, Gel I. M., Gel S. I.

Research output: Contribution to journalArticlepeer-review

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 languageRussian
Pages (from-to)3-26
Number of pages24
JournalUspekhi Matematicheskikh Nauk
Volume28
Issue number3(171)
DOIs
StatePublished - 1973
Externally publishedYes

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