On the Wronskian combinants of binary forms

Given a sequence image of binary d-ics, we construct a set of combinants C={Cq:0≤q≤r,q≠1}, to be called the Wronskian combinants of image. We show that the span of image can be recovered from C as the solution space of an SL(2)-invariant differential equation. The Wronskian combinants define a projective imbedding of the Grassmannian G(r,Sd), and, as a corollary, any other combinant of image is expressible as a compound transvectant in C. Our main result characterises those sequences of binary forms that can arise as Wronskian combinants; namely, they are the ones such that the associated differential equation has the maximal number of linearly independent polynomial solutions. Along the way we deduce some identities which relate Wronskians to transvectants. We also calculate compound transvectant formulae for C in the case r=3.