Crystal Approach to Affine Schubert Calculus

We apply crystal theory to affine Schubert calculus, Gromov–Witten invariants for the complete flag manifold, and the positroid stratification of the positive Grassmannian. We introduce operators on decompositions of elements in the type-$A$ affine Weyl group and produce a crystal reflecting the internal structure of the generalized Young modules whose Frobenius image is represented by stable Schu...