G-exceptional vector bundles on P2 and representations of quivers

It is known that the category of homogeneous bundles on ${\mathbb{P}}^2$ is equivalent to the category of representations of a quiver with relation. In this paper we make use of this equivalence to describe a family of G-exceptional bundles on ${\mathbb{P}}^2$ and to prove that they are stable. We also study the G-exceptionality of Fibonacci bundles on ${\mathbb{P}}^2$.