Homogeneous instanton bundles on P3P3 for the action of SL(2)

We classify kk-instanton bundles on PC3 which are homogeneous for the group SL(2), acting linearly on P3P3 with an open orbit. Besides the classical special instantons, we find isolated examples for SL(2) acting by the representation of binary cubics. We show that these examples are unique and that they exist only for k=a(a−1)/2k=a(a−1)/2, for some a≥2a≥2. We also compute their minimal free resolution in terms of homogeneous equivariant matrices.