Relations in the quantum cohomology ring of G/B

Abstract

The ideal of relations in the (small) quantum cohomology ring of the generalized flag manifold $G/B$ has been determined by B. Kim. We are going to point out a limited number of properties that, if they are satisfied by an $R[q_1,...,q_l]$-bilinear product $\circ$ on $H^{\ast }(G/B)\otimes R[q_1,...,q_l$, then the ring $(H^{\ast }(G/B)\otimes R[q_1,...,q_l],\circ )$ is isomorphic to Kim's ring.

Final version, substantially improved. To appear in Math. Res. Lett