Journal of Lie Theory
Vol. 14, No. 2, pp. 569--581 (2004)
On the principal bundles over a flag manifold
Hassan Azad and Indranil BiswasHassan Azad
Department of Mathematical Sciences
King Fahd University
School of Mathematics
Tata Institute of Fundamental Research
Homi Bhabha Road
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 Harder--Narasimhan 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 $P$.
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Electronic version published on: 1 Sep 2004. This page was last modified: 1 Sep 2004.