Notes on homogeneous vector bundles over complex flag manifolds
| dc.creator | Igonin, Sergei | |
| dc.date | 2002-09-30 | |
| dc.date.accessioned | 2026-07-07T04:51:22Z | |
| dc.date.available | 2026-07-07T04:51:22Z | |
| dc.description | Let P be a parabolic subgroup of a semisimple complex Lie group G defined by a subset Σof simple roots of G, and let E_ϕbe a homogeneous vector bundle over the flag manifold G/P corresponding to a linear representation ϕof P. Using Bott's theorem, we obtain sufficient conditions on ϕin terms of the combinatorial structure of Σfor some cohomology groups of the sheaf of holomorphic sections of E_ϕto be zero. In particular, we define two numbers d(P), l(P) such that for any ϕobtained by natural operations from a representation of dimension less than d(P) the q-th cohomology group of E_ϕis zero for 0<q<l(P). We prove also that in this case the vector bundle E_ϕis rigid. | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/math/0209409 | |
| dc.identifier | http://arxiv.org/abs/math/0209409 | |
| dc.identifier | V.A.Malyshev and A.M.Vershik (eds.), Asymptotic Combinatorics with Application to Mathematical Physics, 245-254. Kluwer, 2002 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65123 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | Representation Theory | |
| dc.subject | 32M10; 32L10; 17B10; 17B20 | |
| dc.title | Notes on homogeneous vector bundles over complex flag manifolds | |
| dc.type | text |