Multivariate hypergeometric functions as \(\tau\)-functions of Toda lattice and Kadomtsev-Petviashvili equation. (English) Zbl 0988.37091
Hypergeometric functions are constructed as \(\tau\)-functions of the Kadomtsev-Petviashvili (KP) hierarchy of equations. The two-dimensional Toda lattice is used to construct hypergeometric functions that depend on many variables, these variables are KP and Toda lattice higher times. The impact of additional symmetries in generating hypergeometric \(\tau\)-functions is briefly discussed.
Reviewer: Samir Musayev (Baku)
MSC:
| 37K20 | Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions |
| 33D80 | Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics |
| 33C80 | Connections of hypergeometric functions with groups and algebras, and related topics |
| 37K05 | Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010) |
| 39A12 | Discrete version of topics in analysis |
| 37K30 | Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures |
Keywords:
Schur polynomial; KP hierarchies; hypergeometric functions; \(\tau\)-functions; Toda latticeReferences:
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