On the Principal Bundles over a Flag Manifold
نویسندگان
چکیده
Let P be a parabolic subgroup of a semisimple simply connected linear algebraic group G over C and ρ an irreducible homomorphism from P to a complex reductive group H . We show that the associated principal H –bundle over G/P , associated for ρ to the principal P –bundle defined by the quotient map G −→ G/P , is stable. We describe the Harder–Narasimhan reduction of the G–bundle over G/P obtained using the composition P −→ L(P ) −→ G , where L(P ) is the Levi factor of P .
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