K-Theoretic J-Functions of Type A Flag Varieties

The J-function in Gromov–Witten theory is a generating function for one-point genus zero Gromov–Witten invariants with descendants. Here, we give formulas for the quantum K-theoretic J-functions of type A flag manifolds. As an application, we prove the quantum K-theoretic J-function version of the abelian–nonabelian correspondence for Grassmannians and products of projective space.