稳定包络、涡旋模空间与Verma模
Stable Envelopes, Vortex Moduli Spaces, and Verma Modules
AI总结：
本文显式构造了涡旋模空间的K理论与椭圆稳定包络，将量子差分方程等同于量子Knizhnik-Zamolodchikov方程，并应用于量子q-Langlands对应的分歧版本。
摘要：
我们显式构造了某些涡旋模空间的K理论和椭圆稳定包络，并将其应用于这些簇中有理曲线的枚举几何。特别地，我们将等变变量中的量子差分方程等同于量子Knizhnik-Zamolodchikov方程，并用几何椭圆R矩阵给出它们的单值性。这些构造中的一个新颖几何特征是，所研究的簇并非全纯辛的，但仍然具有表示论意义。在物理学中，它们源于具有$\mathcal{N} = 2$而非$\mathcal{N} = 4$超对称性的3d超对称规范理论。我们讨论了结果在Aganagic、Frenkel和Okounkov的量子q-Langlands对应的分歧版本中的应用。
英文摘要：
We explicitly construct K-theoretic and elliptic stable envelopes for certain moduli spaces of vortices, and apply this to enumerative geometry of rational curves in these varieties. In particular, we identify the quantum difference equations in equivariant variables with quantum Knizhnik-Zamolodchikov equations, and give their monodromy in terms of geometric elliptic R-matrices. A novel geometric feature in these constructions is that the varieties under study are not holomorphic symplectic, yet nonetheless have representation-theoretic significance. In physics, they originate from 3d supersymmetric gauge theories with $\mathcal{N} = 2$ rather than $\mathcal{N} = 4$ supersymmetry. We discuss an application of the results to the ramified version of the quantum q-Langlands correspondence of Aganagic, Frenkel, and Okounkov.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
