有限非周期Toda格的50年：几何和拓扑观点
Fifty years of the finite nonperiodic Toda lattice: A geometric and topological viewpoint
摘要：
1967年，日本物理学家户田守和在《日本物理学会杂志》上发表了两篇开创性的论文，展示了最近邻粒子之间存在非线性相互作用的粒子链的孤子解。在随后的50年里，户田的质点系被推广到不同的方向，每个方向都有自己的解析、几何和拓扑特征。这些被统称为户田晶格。本综述从几何和拓扑的角度叙述和比较了有限非周期Toda晶格的各种版本。特别是，我们突出的多面体结构的解决方案空间，通过时刻图，我们解释之间的连接真正的不确定户田流和积分上同调真正的标志品种。
英文摘要：
In 1967, Japanese physicist Morikazu Toda published a pair of seminal papers in the Journal of the Physical Society of Japan that exhibited soliton solutions to a chain of particles with nonlinear interactions between nearest neighbors. In the fifty years that followed, Toda's system of particles has been generalized in different directions, each with its own analytic, geometric, and topological characteristics. These are known collectively as the Toda lattice. This survey recounts and compares the various versions of the finite nonperiodic Toda lattice from the perspective of their geometry and topology. In particular, we highlight the polytope structure of the solution spaces as viewed through the moment map, and we explain the connection between the real indefinite Toda flows and the integral cohomology of real flag varieties.
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