SCHUBERT CELLS AND COHOMOLOGY OF THE SPACESG/P

I N Bernstein, I M Gel'fand, S I Gel'fand
1973 Russian Mathematical Surveys  
I. M. Gel'fand, S. I. Gel'fand We study the homological properties of the factor space G/P, where G is a complex semisimple Lie group and Ρ 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 Η of G. The results obtained are used to describe the
more » ... sed to describe the algebraic action of the Weyl group W of G on the cohomology of G/P.
doi:10.1070/rm1973v028n03abeh001557 fatcat:snfnmbspxvh7domjzcjgar5rde