AI 中文总结
该研究描述了量子化BFN库仑分支在局域化映射下的像，给出了类似DAHA构造的根与残差条件，并为量子化锥形库仑分支提供了球迹的数学构造。
AI 中文摘要
我们描述了任意G、N下量子化BFN库仑分支$\boldsymbol{\textit{A}}_{G,N}^{\boldsymbol{\textit{h}}=1}$在局域化（阿贝尔化）映射下的像。对于无环的 quiver 规范理论等多数情形，该描述适用于任意味，有时需取一般或形式味参数。答案由类似Ginzburg—Kapranov—Vasserot构造DAHA（arXiv:alg-geom/9512017）的根与残差条件给出。作为推论，对任意量子化锥形库仑分支（及零或少量味），我们给出了Gaiotto与Okazaki（arXiv:1911.11126）引入的球迹的数学构造。
英文摘要
We describe the image of a quantized BFN Coulomb branch $\mathcal{A}_{G,N}^{\hbar=1}$ under localization (abelianization) map for any $G,N$. In most cases, such as quiver gauge theories without loops, this description works for any flavors, sometimes we need to take generic or formal flavor parameters. The answer is given by a roots and residue condition similar to Ginzburg---Kapranov---Vasserot construction of DAHA arXiv:alg-geom/9512017. As a corollary, for any quantized conical Coulomb branch (and zero or small flavors) we provide a mathematical construction of the sphere trace introduced by Gaiotto and Okazaki arXiv:1911.11126.
Comments15 pages
