Fusion product of co-adjoint orbits

The result contained in this paper is an application of a fixed point formula associated with Hamiltonian loop group action. We obtain a G-space which is a geometric dual of the Verlinde’s fusion product. Also we obtain a proof of Verlinde formula. The calculation of weights at the fixed point set is based on fundamental properties of root systems of affine Lie algebras. This paper was written in early 1997, the current version has a computer time-stamp 4/4/97.