论文标题
异构粒细胞tau函数的单型依赖性和符号几何形状在圆环上
Monodromy dependence and symplectic geometry of isomonodromic tau functions on the torus
论文作者
论文摘要
我们通过使用其明确的Fredholm依赖型代表性来计算具有$ n $ fuchsian奇异性和$ n $ sl（n）$残留矩阵的曲线的异构词的依赖性。我们表明，tau函数的外对数衍生物定义了在单粒子和时间空间上的封闭形式，并通过单构型互轴形肌形态的生成功能进行识别。作为一个说明性的例子，我们详细讨论了单函数圆环的最简单情况。最后，我们表明，可以使用此处介绍的技术以直接的方式恢复在零属中获得的先前结果。
We compute the monodromy dependence of the isomonodromic tau function on a torus with $n$ Fuchsian singularities and $SL(N)$ residue matrices by using its explicit Fredholm determinant representation. We show that the exterior logarithmic derivative of the tau function defines a closed one-form on the space of monodromies and times, and identify it with the generating function of the monodromy symplectomorphism. As an illustrative example, we discuss the simplest case of the one-punctured torus in detail. Finally, we show that previous results obtained in the genus zero case can be recovered in a straightforward manner using the techniques presented here.
