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

点击翻译按钮获取中文摘要

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.