Affine symmetries in quantum cohomology: corrections and new results

In [CMP09] a general formula was given for the multiplication by some special Schubert classes in the quantum cohomology of any homogeneous space. Although this formula is true in the non equivariant setting, the stated equivariant version is wrong. We provide correction for the equivariant formula, thus giving a correct argument for the non equivariant formula.