标题： 量子K环的偏旗流形、库仑分支和贝斯方程 显示英文标题

标题： Quantum K-Rings of Partial Flag Varieties, Coulomb Branches, and the Bethe Ansatz

摘要： 我们给出一个纯粹几何的解释，说明描述旗流形量子$K$理论的三维 GLSM 的库仑分支方程与五顶点格点模型的贝茨假设方程之间的巧合。在这样做时，我们证明了旗流形的量子$K$环的两个显式表示，解决了 Gu-Sharpe-Mihalcea-Xu-Zhang-Zou 和 Rimanyi-Tarasov-Varchenko 的猜想。我们还证明了部分旗流形的稳定映射和准映射$K$理论是同构的，利用 Koroteev-Pushkar-Smirnov-Zeitlin 的工作将后者环与五顶点格点模型的贝茨代数相联系。我们的同构给出了准映射环中描述的量子典范丛更明确的描述。 显示英文摘要

摘要： 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 a more explicit description of the quantum tautological bundles described in the quasimap ring.