Relations in the quantum cohomology ring of $G/B$

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

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Published 1 January 2004