تقرير
Geometry of the Pfaff lattices
| العنوان: | Geometry of the Pfaff lattices |
|---|---|
| المؤلفون: | Kodama, Y., Pierce, V. U. |
| سنة النشر: | 2007 |
| المجموعة: | Nonlinear Sciences |
| مصطلحات موضوعية: | Nonlinear Sciences - Exactly Solvable and Integrable Systems, Mathematical Physics |
| الوصف: | 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 $\tau$-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. Comment: 37 pages, 5 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/0705.0510 |
| رقم الأكسشن: | edsarx.0705.0510 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |