Cohomology algebra of Schubert varieties associated to Kac-Moody groups. (English) Zbl 0591.14037

Kumar, Shrawan

Algebraic geometry, Proc. Conf., Vancouver/B.C. 1984, CMS Conf. Proc. 6, 277-299 (1986).

[For the entire collection see Zbl 0575.00008.]
Let \(G\) and \(P\) be the groups associated to a Kac-Moody Lie-algebra with symmetrizable Cartan matrix and a parabolic subalgebra, respectively. The author announces some results on the cohomology algebra \(H^*(G/P,\mathbb C)\).

Reviewer: Franz Pauer (Innsbruck)

MSC:

14M15	Grassmannians, Schubert varieties, flag manifolds
14F25	Classical real and complex (co)homology in algebraic geometry
17B67	Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
14M17	Homogeneous spaces and generalizations
22E67	Loop groups and related constructions, group-theoretic treatment

Keywords:

cohomology of Schubert varieties; Kac-Moody Lie-algebra

Citations:

Zbl 0575.00008