Quantum Schubert polynomials
Quantum Schubert polynomials
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-Schützenberger theory of Schubert polynomials.We also derive the quantum Monk's formula.