Quantum Schubert polynomials for the G2 flag manifold

We study some combinatorial objects related to the flag manifold X of Lie type G₂. Using the moment graph of X we calculate all the curve neighborhoods for Schubert classes. We use this calculation to investigate the ordinary and quantum cohomology rings of b. As an application, we obtain positive Schubert polynomials for the cohomology ring of X and we find quantum Schubert polynomials which represent Schubert classes in the quantum cohomology ring of X.