On the expansion coefficients of Tau-functions of the KP hierarchy. (English) Zbl 1508.37091
Summary: We study the coefficients of the tau function of the KP hierarchy. If the tau function does not vanish at the origin, it is known that the coefficients are given by Giambelli formula. We introduce a generalization of Giambelli formula to the case when the tau function vanishes at the origin. This paper is a summary of [A. Nakayashiki et al., J. Integrable Syst. 2, Article ID xyx007, 23 p. (2017; Zbl 1397.37076)].
MSC:
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 37K25 | Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry |
| 37K30 | Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures |
