论文标题
$ \ mathfrak {gl} _2（\ Mathbb {c}）$ hamiltonian代表一般有理连接的异构词的变形
Hamiltonian representation of isomonodromic deformations of general rational connections on $\mathfrak{gl}_2(\mathbb{C})$
论文作者
论文摘要
在本文中，我们研究并建立了与任何$ \ Mathfrak {gl} _2（\ Mathbb {C}）$ meromorphic连接的任何$ \ mathfrak {gl} _2（\ Mathfrak {gl} _2（\ mathfrak）的hamiltonian系统，并具有任意数量的任意程度的非符号杆。特别是，我们提出了以与电线杆相关的不规则时间和单粒子以及$ g $ darboux坐标的形式表达的宽松和哈密顿的演变，定义为在操作表中产生的明显奇异性。此外，我们还提供了异构粒细胞变形的减少为$ g $非平整异构粒细胞变形的子集。这种减少等同于地图将不规则时间的集合减少到$ g $非平凡的异散粒度时间。我们将我们的构造应用于所有相关光谱曲线具有属1并恢复标准painlevé方程的情况。我们最终从这个角度与拓扑递归和经典光谱曲线的量化建立了联系。
In this paper, we study and build the Hamiltonian system attached to any $\mathfrak{gl}_2(\mathbb{C})$ meromorphic connection with arbitrary number of non-ramified poles of arbitrary degrees. In particular, we propose the Lax pairs and Hamiltonian evolutions expressed in terms of irregular times and monodromies associated to the poles as well as $g$ Darboux coordinates defined as the apparent singularities arising in the oper gauge. Moreover, we also provide a reduction of the isomonodromic deformations to a subset of $g$ non-trivial isomonodromic deformations. This reduction is equivalent to a map reducing the set of irregular times to only $g$ non-trivial isomonodromic times. We apply our construction to all cases where the associated spectral curve has genus 1 and recover the standard Painlevé equations. We finally make the connection with the topological recursion and the quantization of classical spectral curve from this perspective.
