2024/01/05 by Xiaohan Yan, Yan, Xiaohan
Mathematics · #14N35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2401.03054
openalex publication_date 2024/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this paper, we prove the quantum Serre duality for genus-zero K-theoretic permutation-invariant Gromov-Witten theory. The formulation of the theorem relies on an extension to the formalism of loop spaces and big J-functions more intrinsic to quantum K-theory. With the extended formalism, we also arrive at a re-interpretation of the level structures in terms of twisted quantum K-theories. We discuss the torus-equivariant theory in the end, and as an application generalize the K-theoretic quantum Serre duality to non-primitive vector bundles over flag varieties.