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arXiv · 0903.4399

Homogeneous principal bundles and stability

Indranil Biswas
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Abstract

Let G/P be a rational homogeneous variety, where P is a parabolic subgroup of a simple and simply connected linear algebraic group G defined over an algebraically closed field of characteristic zero. A homogeneous principal bundle over G/P is semistable (respectively, polystable) if and only if it is equivariantly semistable (respectively, equivariantly polystable). A stable homogeneous principal H-bundle (E_H ,ρ) is equivariantly stable, but the converse is not true in general. If a homogeneous principal H-bundle (E_H ,ρ) is not equivariantly stable but not stable, then E_H admits an action ρ' of G such that the pair (E_H ,ρ') is a homogeneous principal H-bundle which is not equivariantly stable.

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Indranil Biswas. 2009-03-25. Homogeneous principal bundles and stability. https://arxiv.org/abs/0903.4399

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