The Kademtsev-Petviashvily (KP) equation is a famous evolution equation with soliton solutions. It was discovered by M.Sato and the Kyoto school that the KP equation can be regarded as a part of a countable system of compatible evolution equations, which is called today the KP hierarchy. The observation allowed the researchers to discover many new examples of soliton type hierarchies and to study them with methods of mathematical physics, algebraic geometry and representation theory. In the talk we will describe the explicit construction of polynomial tau-functions of the KP, BKP hierarchies through their generating functions. The method uses the tools of representation theory and properties of symmetric functions.
The talk is based on the joint work with V. G. Kac and J. van de Leur.
This video was produced by the Universidade de São Paulo, as part of the LieJor Online Seminar: Algebras, Representations, and Applications.
