  In this article we give formulas for the Riemann-Roch number of a symplectic
quotient arising as the reduced space corresponding to a coadjoint orbit (for
an orbit close to 0) as an evaluation of cohomology classes over the reduced
space at 0. This formula exhibits the dependence of the Riemann-Roch number on
the Lie algebra variable which specifies the orbit. We also express the formula
as a sum over the components of the fixed point set of the maximal torus. Our
proof applies to Hamiltonian G-manifolds even if they do not have a compatible
Kahler structure, using the definition of quantisation in terms of the Spin-C
Dirac operator.
