Journal of Lie Theory

no. 2
On the Principal Bundles over a Flag Manifold<!-- Anfang Autor -->
Journal of Lie Theory, Volume 14 (2004) no. 2, pp. 569-581
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 $P$.
DOI: 10.5802/jolt.354
Classification: 14M15, 20G05, 17B45, 14L24, 14J60, 53C07
Keywords: parabolic subgroup, stable bundle, Harder-Narasimhan reduction 
@article{JOLT_2004_14_2_a14,
     author = {H. Azad and I. Biswas},
     title = {On the {Principal} {Bundles} over a {Flag} {Manifold<!--} {Anfang} {Autor} -->},
     journal = {Journal of Lie Theory},
     pages = {569--581},
     year = {2004},
     volume = {14},
     number = {2},
     doi = {10.5802/jolt.354},
     zbl = {1080.14055},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.354/}
}
TY  - JOUR
AU  - H. Azad
AU  - I. Biswas
TI  - On the Principal Bundles over a Flag Manifold
JO  - Journal of Lie Theory
PY  - 2004
SP  - 569
EP  - 581
VL  - 14
IS  - 2
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.354/
DO  - 10.5802/jolt.354
ID  - JOLT_2004_14_2_a14
ER  - 
%0 Journal Article
%A H. Azad
%A I. Biswas
%T On the Principal Bundles over a Flag Manifold
%J Journal of Lie Theory
%D 2004
%P 569-581
%V 14
%N 2
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.354/
%R 10.5802/jolt.354
%F JOLT_2004_14_2_a14
H. Azad; I. Biswas. On the Principal Bundles over a Flag Manifold. Journal of Lie Theory, Volume 14 (2004) no. 2, pp. 569-581. doi: 10.5802/jolt.354

Cited by Sources: