Journal of Lie Theory Vol. 14, No. 2, pp. 569581 (2004) 

On the principal bundles over a flag manifoldHassan Azad and Indranil BiswasHassan AzadDepartment of Mathematical Sciences King Fahd University Dhahran 31261 Saudi Arabia hassanaz@kfupm.edu.sa and Indranil Biswas School of Mathematics Tata Institute of Fundamental Research Homi Bhabha Road Bombay 400005 India indranil@math.tifr.res.in Abstract: Let $P$ be a parabolic subgroup of a semisimple simply connected linear algebraic group $G$ over $\mathbb C$ and $\rho$ an irreducible homomorphism from $P$ to a complex reductive group $H$. We show that the associated principal $H$bundle over $G/P$, associated for $\rho$ to the principal $P$bundle defined by the quotient map $G\, \longrightarrow\, G/P$, is stable. We describe the HarderNarasimhan reduction of the $G$bundle over $G/P$ obtained using the composition $P\, \longrightarrow\, L(P)\, \longrightarrow\, G$, where $L(P)$ is the Levi factor of $P$. Full text of the article:
Electronic version published on: 1 Sep 2004. This page was last modified: 1 Sep 2004.
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