Pfaff格的几何
Geometry of the Pfaff lattices
摘要：
Pfaff格是Adler和van Moerbeke为了描述GOE和GSE型随机矩阵模型的配分函数而引入的。这些矩阵模型的配分函数由称为矩矩阵的某些斜对称矩阵的Pfaff变换给出，并且它们是Pfaff格的$τ$-函数。在本文中，我们研究了有限版本的Pfaff格点方程作为一个哈密顿系统。特别地，我们证明了Arnold-Liouville意义上的完全可积性，并使用矩映射，我们描述了真正的等谱品种的Pfaff格。矩映射的图像是凸多面体，其顶点被确定为由Pfaff格生成的流的不动点。
英文摘要：
Pfaff lattice was introduced by Adler and van Moerbeke to describe the partition functions for the random matrix models of GOE and GSE type. The partition functions of those matrix models are given by the Pfaffians of certain skew-symmetric matrices called the moment matrices, and they are the $τ$-functions of the Pfaff lattice. In this paper, we study a finite version of the Pfaff lattice equation as a Hamiltonian system. In particular, we prove the complete integrability in the sense of Arnold-Liouville, and using a moment map, we describe the real isospectral varieties of the Pfaff lattice. The image of the moment map is a convex polytope whose vertices are identified as the fixed points of the flow generated by the Pfaff lattice.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
