Abstract: Let G be a simply connected, simple linear algebraic group, P a parabolic subgroup and X the quotient of G by P. The moduli space of three pointed genus zero stable maps to X is quasi-homogeneous under the action of the automorphism group of X for all minimal degrees in quantum products. In this talk, we construct a distinguished morphism which gives an open dense orbit. The construction of this morphism is based on orthogonality relations in greedy decompositions of minimal degrees in quantum products.