论文标题
广义高压法的模量空间
Moduli spaces of generalized hyperpolygons
论文作者
论文摘要
我们介绍了广义高层分析的概念，该概念是作为中岛的一种代表，是一种彗星形颤抖的意义。我们以刚性几何形状数字（即多边形对：一个紧凑型基团的谎言代数，另一个是络合物中的代数）来识别这些表示形式。对于此类数据，我们将明显的Meromorormormormormormormormormormormormorormormormormorormormormormormorormorphic Higgs捆绑在一个属-g $ Riemann Surface，其中$ G $是彗星中的回路数，从而将Nakajima Quiver品种嵌入了刺激的Hitchin系统中，将其嵌入了刺激的属属 - $ G $ G $ G $ Riemann Surface（通常与阳性法规）。我们表明，在某些关于标志类型的假设下，广义高层分析的空间承认了完全可以整合的gelfand-tsetlin类型的汉密尔顿系统的结构，该结构是从偏向旗品种的减少继承而来的。在所有旗帜都完成的情况下，我们介绍了哈密顿人。我们还评论了由高血压法给出的Hitchin方程的离散化，三重麸皮的构建（从Kapustin-Witten-witten-witten镜面对称性）以及Tame和Wild Hitchin Systems之间的二重性（从PainlevéBrainlevé超越的意义上）。
We introduce the notion of generalized hyperpolygon, which arises as a representation, in the sense of Nakajima, of a comet-shaped quiver. We identify these representations with rigid geometric figures, namely pairs of polygons: one in the Lie algebra of a compact group and the other in its complexification. To such data, we associate an explicit meromorphic Higgs bundle on a genus-$g$ Riemann surface, where $g$ is the number of loops in the comet, thereby embedding the Nakajima quiver variety into a Hitchin system on a punctured genus-$g$ Riemann surface (generally with positive codimension). We show that, under certain assumptions on flag types, the space of generalized hyperpolygons admits the structure of a completely integrable Hamiltonian system of Gelfand-Tsetlin type, inherited from the reduction of partial flag varieties. In the case where all flags are complete, we present the Hamiltonians explictly. We also remark upon the discretization of the Hitchin equations given by hyperpolygons, the construction of triple branes (in the sense of Kapustin-Witten mirror symmetry), and dualities between tame and wild Hitchin systems (in the sense of Painlevé transcendents).
