The description of cohomology tables in Boij-Soederberg theory can be thought of as saying that an arbitrary vector bundle on P^n "looks like" a certain homogeneous bundle (that is, one made from a representation of GL_n applied to the tangent bundle). I will explain this connection, and a new application of the philosophy that leads to sharp statements about the vanishing of cohomology of tensor products of bundles on P^n. This is all joint work with Frank Schreyer.