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arXiv · 2507.15183

A Nakayama result for the quantum K theory of homogeneous spaces

Wei Gu·Leonardo C. Mihalcea·Eric Sharpe·Weihong Xu·Hao Zhang·Hao Zou
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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.

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Wei Gu, Leonardo C. Mihalcea, Eric Sharpe, Weihong Xu, Hao Zhang, Hao Zou. 2025-07-21. A Nakayama result for the quantum K theory of homogeneous spaces. https://doi.org/10.46298/epiga.2025.17016

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