标题： 量子K环的偏旗流形、库仑分支和贝瑟假设 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3D GLSM中的库仑分支方程与五顶点格子模型的Bethe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$K$环的一个显式表示，解决了Gu-Sharpe-Mihalcea-Xu-Zhang-Zou的猜想。我们还给出了该环与五顶点格子模型的Bethe代数的识别，这证明了部分旗流形的稳定映射和准映射$K$理论是同构的。这种同构也提供了后者环中出现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 an explicit presentation for the quantum $K$-ring of the flag variety, resolving a conjecture of Gu-Sharpe-Mihalcea-Xu-Zhang-Zou. We also give an identification of the ring with the Bethe algebra of the 5-vertex lattice model, which proves that the stable map and quasimap $K$-theory of the partial flag varieties are isomorphic. This isomorphism also provides a more explicit description of the quantum tautological bundles that appear in the latter ring.