斜和与有向图规范场理论
Slant sums of quiver gauge theories
AI总结：
研究斜和操作在有向图规范场理论中的定义与应用，通过扭矩固定点关系及分支规则推导出因子化结论，提出关于Coulomb分支的猜想并验证ADE类型情况。
摘要：
我们定义了有向图规范场理论的斜和，这是一种在底层有向图上粘合的操作，将规范顶点与框架顶点识别。在某些温和假设下，我们将对应的Higgs分支上的扭矩固定点，这些是Nakajima有向图变种。然后我们证明了一个"分支规则"，将斜和前后准映射顶点函数联系起来，并推导出若干"因子化"推论。我们的构造受零维有向图变种顶点函数因子化猜想的启发，可以使用分支规则归纳法进行研究。在特殊情况下，它还表明顶点函数可以表示为反平面分区的和，即使在ADE类型之外。我们为Coulomb分支提出了一些猜想，反映了Higgs侧所见的内容，并在ADE类型中证明了它们。特别是，我们得到了所谓的"极值"不可约模块在移位Yangians上的精细特征公式。我们还研究了Coulomb分支的斜和及其量子化。我们观察到对于一维框架，Coulomb分支的斜和等同于乘积。
英文摘要：
We define the slant sum of quiver gauge theories, a gluing on the underlying quivers that identifies a gauge vertex with a framing vertex. Under some mild assumptions, we relate torus fixed points on the corresponding Higgs branches, which are Nakajima quiver varieties. Then we prove a ``branching rule" relating the quasimap vertex functions before and after a slant sum and deduce a number of ``factorization" corollaries. Our construction is motivated by a factorization conjecture for the vertex functions of zero-dimensional quiver varieties, which can be approached inductively using the branching rule. In special cases, it also shows that vertex functions can be written as sums over reverse plane partitions, even outside ADE type. We make some conjectures for Coulomb branches reflecting what can be seen on the Higgs side and prove them in ADE type. In particular, we obtain refined character formulas for the so-called ``extremal'' irreducible modules over shifted Yangians. We also study slant sums of Coulomb branches and their quantizations. We observe that for one-dimensional framing, the slant sum of Coulomb branches is the same as the product.
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