论文标题
异构果etau作为弗雷德尔姆决定因素在圆环上起作用，并带电分区
Isomonodromic tau functions on a torus as Fredholm determinants, and charged partitions
论文作者
论文摘要
我们证明，在$ gl（n，\ mathbb {c}）$中具有紫红色奇异性和通用单粒子的圆环上的异构词，可以用弗雷姆（Fredholm）的cauchy-plemelj操作员的决定来编写。我们进一步表明，这种弗雷德尔姆决定因素的次要扩展是由带电分区标记的系列描述的。例如，我们表明，在$ sl（2，\ mathbb {c}）的情况下，此组合表达式采用双nekrasov-okounkov分区函数的形式，或者在圆环上等效地等同于免费的费米子结构块。基于这些结果，我们还提出了Riemann-Hilbert问题的Tau功能的定义，该问题在A-Cycle上具有通用跳跃的圆环。
We prove that the isomonodromic tau function on a torus with Fuchsian singularities and generic monodromies in $GL(N,\mathbb{C})$ can be written in terms of a Fredholm determinant of Cauchy-Plemelj operators. We further show that the minor expansion of this Fredholm determinant is described by a series labeled by charged partitions. As an example, we show that in the case of $SL(2,\mathbb{C})$ this combinatorial expression takes the form of a dual Nekrasov-Okounkov partition function, or equivalently of a free fermion conformal block on the torus. Based on these results, we also propose a definition of the tau function of the Riemann-Hilbert problem on a torus with generic jump on the A-cycle.
