Loop Grassmannian cohomology, the principal nilpotent and Kostant theorem

Details Loop Grassmannian cohomology, the principal nilpotent and Kostant theorem Loop Grassmannian cohomology, the principal nilpotent and Kostant theorem

1998-03-30

arxiv.org/abs/math/9803141v2

Mathematics

Algebraic Geometry

10 pages, LaTeX2e. lemma 4.6 added, title changed, and several misprints corrected

Scientific paper

Given a complex projective algebraic variety, write H(X) for its cohomology with complex coefficients and IH(X) for its Intersection cohomology. We first show that, under some fairly general conditions, the canonical map H(X)\to IH(X) is injective. Now let Gr = G((z))/G[[z]] be the loop Grassmannian for a complex semisimple group G, and let X be the closure of a G[[z]]-orbit in Gr. We prove, using the general result above, a conjecture of D. Peterson describing the cohomology algebra H(X) in terms of the centralizer of the principal nilpotent in the Langlands dual of Lie(G). In the last section we give a new "topological" proof of Kostant's theorem about the polynomial algebra of a semisimple Lie algebra, based on purity of the equivariant intersection cohomology groups of G[[z]]-orbits on Gr.

Affiliated with

Also associated with

No associations

Rating

Loop Grassmannian cohomology, the principal nilpotent and Kostant theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Loop Grassmannian cohomology, the principal nilpotent and Kostant theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Loop Grassmannian cohomology, the principal nilpotent and Kostant theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-110921