Cohomological characterization of vector bundles on Grassmannians of lines

We introduce a notion of regularity for coherent sheaves on Grassmannians of lines. We use this notion to prove some extension of Evans–Griffith criterion to characterize direct sums of line bundles. We also give, in the line of previous results by Costa and Miró-Roig, a cohomological characterization of exterior and symmetric powers of the universal bundles of the Grassmannian.