A Nakayama result for the quantum K theory of homogeneous spaces

Abstract

We prove that the ideal of relations in the (equivariant) quantum K ring of a homogeneous space is generated by quantizations of each of the generators of the ideal in the classical (equivariant) K ring. This extends to quantum K theory a result of Siebert and Tian in quantum cohomology. We illustrate this technique in the case of the quantum K ring of partial flag manifolds, using a set of quantum K Whitney relations conjectured by the authors, and recently proved by Huq-Kuruvilla.