2021/06/11 by Xiaohan Yan, Yan, Xiaohan
Mathematics · Physics and Astronomy · #14N35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2106.06281
openalex publication_date 2021/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we reconstruct explicitly the generating function of genus-zero K-theoretic permutation-invariant Gromov-Witten invariants, known as the big J-function, for any partial flag variety. The reconstruction may start with any Weyl-group-invariant value of the well-understood big J-function of an associated toric variety. We generalize the recursive method \citeGivental:perm2, based on torus fixed point localization, to deal with non-isolated one-dimensional toric orbits, through incorporating ``balanced broken orbits'' into consideration and subsequently proving a vanishing result of their contribution. Furthermore, we extend the study to twisted generating functions of the flag variety, and demonstrate properties including a non-abelian quantum Lefschetz theorem and a duality between level structures. In the end, we construct a K-theoretic mirror in terms of Jackson-type integrals.