Hook Multiplication in the Quantum K-Theory of Grassmannians

TL;DR

This paper develops a positive formula for multiplying classes by hook classes in the quantum K-theory ring of Grassmannians, extending previous Pieri rules and providing combinatorial insights.

Contribution

It introduces a new positive formula for hook multiplication in quantum K-theory of Grassmannians, generalizing the Pieri rule and offering a combinatorial interpretation.

Findings

Derived a manifestly positive formula for hook class products

Extended the quantum K-theoretic Pieri rule

Provided a combinatorial interpretation of the formula

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.