Geodesic
On simple and stable homogeneous bundles
Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 1, pp. 51-67

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Zbl MR
In this work we will analyze the relation between the stability and the simplicity of a homogeneous vector bundle on a projective variety. Our main theorem shows that a homogeneous bundle is not destabilized by its homogeneous subbundles if and only if it is the tensor product of a stable homogeneous bundle and an irreducible representation. Then we give an example of a homogeneous bundle, which is simple, but not stable. 
Faini, Simona. On simple and stable homogeneous bundles. Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 1, pp. 51-67. http://geodesic.mathdoc.fr/item/BUMI_2006_8_9B_1_a2/
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     author = {Faini, Simona},
     title = {On simple and stable homogeneous bundles},
     journal = {Bollettino della Unione matematica italiana},
     pages = {51--67},
     year = {2006},
     volume = {Ser. 8, 9B},
     number = {1},
     zbl = {1178.14012},
     mrnumber = {MR2204900},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2006_8_9B_1_a2/}
}
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