Factorisation of generalised theta functions II: The Verlinde formula

Given a projective G-variety V (G a reductive group) and an ample bundle \̂gq linearising the G-action, we relate the invariant cohomology (with values in \̂gq) of V with that of the open set Vss of semistable points. We use this to extend established results, to prove the Verlinde formula for the dimension of the space of sections of these bundles on the moduli spaces of (parabolic, rank 2) vector bundles on a complex projective curve.