1973/06/30 by I N Bernstein, I. N. Bernstein, I M Gel'fand +3 · 323 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebra over a field #Algebraic group #Algebraic number #Cohomology #Combinatorics #Equivariant cohomology #Geometry and complex manifolds #Group cohomology #Lie algebra #Mathematical analysis #Mathematics #Partition (number theory) #Pure mathematics
paper · doi:10.1070/rm1973v028n03abeh001557
published in Russian Mathematical Surveys 28(3), 1-26 (IOP Publishing)
crossref issued 1973/06/30 · crossref published 1973/06/30 · crossref published-print 1973/06/30 · openalex publication_date 1973/06/30 · crossref created 2005/11/08 · crossref published-online 2007/10/16 · crossref deposited 2024/10/03 · openalex created_date 2025/10/10 · crossref indexed 2026/07/29 · openalex updated_date 2026/07/31
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 .