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

本课题研究了以旗簇的大胞元以外的胞元为参数的户田格的解。利用旗簇的Bruhat分解得到了户田格的解.对于任意旗簇的胞腔，通过Bruhat分解，可以得到户田格的解.然而，由这种分解得到的Lax算子一般不是三对角型（Jacobi元）。大约20年前Kostant表明，Bruhat分解的大细胞给出了拉克斯算子的雅可比元素。本文证明了另一个胞元的Bruhat分解给出了Jacobi元的Lax算子。

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.