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In this paper, we compute Gromov-Witten invariants of the flag manifold using a new combinatorial construction for its quantum cohomology ring. Our construction provides quantum analogues of the Bernstein-Gelfand-Gelfand results on the cohomology of the flag manifold, and the Lascoux-Schtzenberger theory of Schubert polynomials. We also derive the quantum Monk's formula.
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Fomin et al. (1997) studied this question.
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