Abstract
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 ) .
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