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

Abstract

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