TY - JOUR
T1 - Schubert cells, and the cohomology of the spaces G/P
T2 - КЛЕТКИ ШУБЕРТА И КОГОМОЛОГИИ ПРОСТРАНСТВ О/Р
AU - Bernštein, I. N.
AU - M., Gel I.
AU - I., Gel S.
N1 - English translation: Russian Mathematical Surveys(1973),28(3):1
PY - 1973
Y1 - 1973
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84911957164&partnerID=8YFLogxK
U2 - 10.1070/RM1973v028n03ABEH001557
DO - 10.1070/RM1973v028n03ABEH001557
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
SN - 0042-1316
VL - 28
SP - 3
EP - 26
JO - Uspekhi Matematicheskikh Nauk
JF - Uspekhi Matematicheskikh Nauk
IS - 3(171)
ER -