2024/09/23 by Irit Huq-Kuruvilla, Huq-Kuruvilla, Irit · 1 citation
Mathematics · #14N35 (Primary) #20C35 (Secondary) #81T30 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Representation Theory (math.RT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2409.15575
openalex publication_date 2024/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a purely geometric explanation of the coincidence between the Coulomb Branch equations for the 3D GLSM describing the quantum K-theory of a flag variety, and the Bethe Ansatz equations of the 5-vertex lattice model. In doing so, we prove two explicit presentations for the quantum K-ring of the flag variety, resolving conjectures of Gu-Sharpe-Mihalcea-Xu-Zhang-Zou and Rimanyi-Tarasov-Varchenko. We also prove that the stable map and quasimap K-theory of the partial flag varieties are isomorphic, using the work of Koroteev-Pushkar-Smirnov-Zeitlin identifying the latter ring with the Bethe algebra of the 5-vertex lattice model. Our isomorphism gives an additional interpretation of the quantum tautological bundles described in the quasimap ring.