On equivariant quantum cohomology of homogeneous spaces: Chevalley formulae and algorithms

We prove a Chevalley formula for the equivariant quantum multiplication of two Schubert classes in the homogeneous variety X=G/P. Using this formula, we give an effective algorithm to compute the 3-point, genus zero, equivariant Gromov-Witten invariants on X, which are the structure constants of its equivariant quantum cohomology algebra