A Nakayama result for the quantum K theory of homogeneous spaces

2025/07/21 by Wei Gu, Leonardo C. Mihalcea, Eric Sharpe +3 · 2 citations
Mathematics · #math.AG #math.CO

paper · pdf · doi:10.46298/epiga.2025.17016

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.

Citations

• Quantum K-theory of Grassmannians
• Quantum K -theory, I: Foundations

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• Quantum K-theoretic Whitney relations for type C flag manifolds
• Schubert line defects in 3d GLSMs, part I: Complete flag manifolds and quantum Grothendieck polynomials
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Related

• Quantum K Whitney relations for partial flag varieties
• A presentation of the torus-equivariant quantum K-theory ring of flag manifolds of type A, Part I: the defining ideal
• Quantum K -theory, I: Foundations
• Quantum K-theoretic Whitney relations for type C flag manifolds
• Quantum K theory for flag varieties