Polynomial tau functions of symplectic KP and multi-component symplectic KP hierarchies. (English) Zbl 1511.37078
The authors study the multi-component symplectic KP hierarchy. In particular, they show that the polynomial tau-function of the symplectic KP hierarchy can be realised as a zero mode of a certain combinatorial generating function. This result is then extended to the multi-component symplectic KP hierarchy. Furthermore, the authors express the polynomial tau-function of the multi-component symplectic KP hierarchy as a determinant. Some Vandermonde-like identities are used for this purpose.
Reviewer: Nenad Manojlović (Faro)
MSC:
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 37K20 | Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions |
| 17B65 | Infinite-dimensional Lie (super)algebras |
| 17B67 | Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras |
| 17B80 | Applications of Lie algebras and superalgebras to integrable systems |
Keywords:
symplectic Schur functions; polynomial tau-functions; symplectic KP hierarchy; multi-component SKP hierarchyReferences:
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