  The moduli space M(n,d) is an algebraic variety parametrizing those
representations of the fundamental group of a punctured Riemann surface into
the Lie group SU(n) for which a loop around the boundary is sent to the n-th
root of unity exp (2 \pi i d/n) multiplied by the identity matrix. If n and d
are coprime it is in fact a K\"ahler manifold. One may relax the constraint and
study moduli spaces M(L) parametrizing those representations for which the loop
around the boundary is sent to an element conjugate to L, if L is some element
in SU(n), and these are also K\"ahler manifolds for a suitable class of L.
  The Verlinde formula calculates the dimension of the space of holomorphic
sections of certain line bundles over the spaces M(n,d) and M(L). We recall how
a new proof of the Verlinde formula for M(n,d) given in joint work with Frances
Kirwan may be obtained, and show how to modify this proof to obtain a proof of
the variant of the Verlinde formula which applies to M(L) (the moduli space of
parabolic bundles with one marked point) and to the analogous object with b
marked points.
