Stability of homgeneous bundles on P^3

We study the stability and the simplicity of some homogeneous bundles on P^3 by using the quiver associated to homogeneous bundles introduced by Bondal and Kapranov. In particular we show that the homogeneous bundles on P^3 whose quiver support is a parallelepiped or a classical staircase are stable. For instance the bundles E whose minimal free resolution is of the kind 0 \rightarrow S^{a_1, a_2, a_3 } V (t) \rightarrow S^{a_1+s, a_2, a_3 } V (t+s) \rightarrow E \rightarrow 0 are stable.