Notes on homogeneous vector bundles over complex flag manifolds

Details Notes on homogeneous vector bundles over complex flag manifolds Notes on homogeneous vector bundles over complex flag manifolds

2002-09-30

arxiv.org/abs/math/0209409v1

V.A.Malyshev and A.M.Vershik (eds.), Asymptotic Combinatorics with Application to Mathematical Physics, 245-254. Kluwer, 2002

Mathematics

Algebraic Geometry

9 pages

Scientific paper

Let P be a parabolic subgroup of a semisimple complex Lie group G defined by a subset \Sigma of simple roots of G, and let E_\phi be a homogeneous vector bundle over the flag manifold G/P corresponding to a linear representation \phi of P. Using Bott's theorem, we obtain sufficient conditions on \phi in terms of the combinatorial structure of \Sigma for some cohomology groups of the sheaf of holomorphic sections of E_\phi to be zero. In particular, we define two numbers d(P), l(P) such that for any \phi obtained by natural operations from a representation of dimension less than d(P) the q-th cohomology group of E_\phi is zero for 0

Affiliated with

Also associated with

No associations

Rating

Notes on homogeneous vector bundles over complex flag manifolds 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 Notes on homogeneous vector bundles over complex flag manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Notes on homogeneous vector bundles over complex flag manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-694137