Abstract: In 1967, Japanese physicist Morikazu Toda proposed an integrable lattice model to describe motions of a chain of particles with exponential interactions between nearest neighbors. Since then, Toda lattice becomes the test ground for various techniques and philosophies in integrable systems and they have been analyzed from the perspectives of analysis, geometry, combinatorics, representation theory etc. 

The full Kostant-Toda lattice is a natural generalization of the original tridiagonal Toda lattice. In this talk, I will show you how to construct rational solutions of the full Kostant-Toda lattice of type B in terms of the Schur polynomials and the Schur-Q polynomials. This talk is based on joint work with Yuji Kodama.