论文标题
抛物线式希格斯束，真实结构和集成性的概括
Generalizations of parabolic Higgs bundles, real structures and integrability
论文作者
论文摘要
我们介绍了一个准抗对称的higgs $ g $ $ g $捆绑的概念，并带有明显的点。它们具有其他结构，这些结构取代了抛物线式希格斯束的标记点处的抛物线结构。后者意味着连接轨道连接到标记点。抛物线Higgs束的模量空间是复杂完全集成系统的相位空间。在我们的情况下，共同聚合轨道被一些特殊的对称空间上的cotangent束取代，以使修改后的希格斯捆绑包的模量空间仍然是复杂完全集成系统的相位空间。我们表明，抛物线式希格斯束的模量空间是准抗对称性希格斯束的模量空间相对于cartan子组产物的作用。同样，通过更改对称空间，我们引入了准连接和准正常的希格斯束。然后，作用在模量空间上的真实参与的固定点集是实际完全集成系统的相位空间。给出了几个示例，包括$ {\ rm sl}（2）$ euler-arnold上衣，两体椭圆形的calogero-moser系统和合理$ {\ rm sl}（2）$ gaudin系统以及其真正的减少。
We introduce a notion of quasi-antisymmetric Higgs $G$-bundles over curves with marked points. They are endowed with additional structures, which replace the parabolic structures at marked points in the parabolic Higgs bundles. The latter means that the coadjoint orbits are attached to the marked points. The moduli spaces of parabolic Higgs bundles are the phase spaces of complex completely integrable systems. In our case the coadjoint orbits are replaced by the cotangent bundles over some special symmetric spaces in such a way that the moduli space of the modified Higgs bundles are still phase spaces of complex completely integrable systems. We show that the moduli space of the parabolic Higgs bundles is the symplectic quotient of the moduli space of the quasi-antisymmetric Higgs bundle with respect to the action of product of Cartan subgroups. Also, by changing the symmetric spaces we introduce quasi-compact and quasi-normal Higgs bundles. Then the fixed point sets of real involutions acting on their moduli spaces are the phase spaces of real completely integrable systems. Several examples are given including integrable extensions of the ${\rm SL}(2)$ Euler-Arnold top, two-body elliptic Calogero-Moser system and the rational ${\rm SL}(2)$ Gaudin system together with its real reductions.
