Rational solutions of Toda lattice parameterized by points of the cells other than the big one of flag variety.

户田晶格的有理解由除旗形大点之外的单元点参数化。

• 批准号: 13640218
• 负责人: IKEDA Kaoru
• 金额: $ 0.7万
• 依托单位: Keio University (2002)Kumamoto University (2001)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640218/
• 关键词: Toda lattice; Flag manifold; Lax operator; Bruhat decomposition; Rieman-Hilbert decomposition; Brnhat分解; Weyl群

In this project we study the solution of Toda lattice which is parameterized by the points of the cell other than the big one of the flag variety. The solution of the Toda lattice is obtained by the Bruhat decomposition of flag variety. For any cells of flag variety, one can obtain the solutions of Toda lattice by Bruhat decomposition. However the Lax operator obtained by this decomposition is not type of tri diagonal (Jacobi element) in general. About 20 years ago Kostant showed that the Bruhat decomposition of the big cell gives the Lax operator of Jacobi element. In this project we show that the Bruhat decomposition of anther cells give the Lax operator of Jacobi element.

在这个项目中，我们研究了Toda格子的解，它是由晶胞上的点来参数化的，而不是用旗子簇中的大点来参数化。Toda格的解是通过FLAG簇的Bruhat分解得到的。对于任何FLAG簇的胞格，都可以通过Bruhat分解得到Toda格解。然而，通过这种分解得到的Lax算子通常不是三对角线(雅可比元素)类型。大约20年前，Kostant证明了大细胞的Bruhat分解给出了雅可比元素的松弛算符。在这个项目中，我们证明了花药细胞的Bruhat分解给出了Jacobi元的Lax算子。

项目成果

池田 薫: "On the Spectral vesolution of the quantum tola lattice"Journal of functional analysis. 185. 404-424 (2001)

池田薰：“论量子托拉晶格的光谱解析”泛函分析杂志 185. 404-424 (2001)。

池田 薫: "On the spectral resolution of the guantum Toda lattice"Journal of functional analysis. 185. 404-424 (2001)

池田薰：“论户田量子点阵的光谱分辨率”泛函分析杂志 185. 404-424 (2001)。