Journal of Lie Theory

no. 3
On the Principal Bundles over a Flag Manifold: II
Journal of Lie Theory, Volume 17 (2007) no. 3, pp. 669-684
[Part I of this article has been published in J. Lie Theory 14 (2004) 569--581.] Let $G$ be a connected semisimple linear algebraic group defined over an algebraically closed field $k$ and $P\subset G$, $P\ne G$, a reduced parabolic subgroup that does not contain any simple factor of $G$. Let $\rho : P\longrightarrow H$ be a homomorphism, where $H$ is a connected reductive linear algebraic group defined over $k$, with the property that the image $\rho(P)$ is not contained in any proper parabolic subgroup of $H$. We prove that the principal $H$-bundle $G\times^P H$ over $G/P$ constructed using $\rho$ is stable with respect to any polarization on $G/P$. When the characteristic of $k$ is positive, the principal $H$-bundle $G\times^P H$ is shown to be strongly stable with respect to any polarization on $G/P$.
DOI: 10.5802/jolt.469
Classification: 14M15, 14F05
Keywords: Homogeneous space, principal bundle, Frobenius, stability 
@article{JOLT_2007_17_3_a14,
     author = {H. Azad and I. Biswas},
     title = {On the {Principal} {Bundles} over a {Flag} {Manifold:} {II}},
     journal = {Journal of Lie Theory},
     pages = {669--684},
     year = {2007},
     volume = {17},
     number = {3},
     doi = {10.5802/jolt.469},
     zbl = {1155.14035},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.469/}
}
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H. Azad; I. Biswas. On the Principal Bundles over a Flag Manifold: II. Journal of Lie Theory, Volume 17 (2007) no. 3, pp. 669-684. doi: 10.5802/jolt.469

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