Let P be a parabolic subgroup of a semisimple simply connected linear algebraic group G over C and an irreducible homomorphism from P to a complex reductive group H .We show that the associated principal H -bundle over G/P , associated for 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 .
Azad et al. (Thu,) studied this question.