On homogeneous vector bundles

Biswas, Indranil ; Subramanian, S. (2008) On homogeneous vector bundles Bulletin des Sciences Mathematiques, 132 (5). pp. 419-424. ISSN 0007-4497

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S00074...

Related URL: http://dx.doi.org/10.1016/j.bulsci.2008.02.002


Let G be a simply connected linear algebraic group, defined over the field of complex numbers, whose Lie algebra is simple. Let P be a proper parabolic subgroup of G. Let E be a holomorphic vector bundle over G/P such that E admits a homogeneous structure. Assume that E is not stable. Then E admits a homogeneous structure with the following property: There is a nonzero subbundle F⊆E left invariant by the action of G such that degree(F)/rank(F)≥ degree(E)/rank(E).

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Homogeneous space; Vector bundle; Stability
ID Code:3584
Deposited On:12 Oct 2010 04:33
Last Modified:12 Oct 2010 04:33

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