Hook Multiplication in the Quantum K-Theory of Grassmannians

Abstract

We study the quantum K-theory ring $QK(X)$ of a Grassmannian $X$ and prove a manifestly positive formula for the product of an arbitrary class by a hook class. This generalizes the quantum K-theoretic Pieri rule, a prior result of Buch and Mihalcea. We also present a combinatorial interpretation of this result.