Representations of sl(n,\({\mathbb{C}})\) and the Toda lattice. (English) Zbl 0645.58024
This work builds on that of Adler and Moerbeke and shows that the linearization procedure for the flows of the periodic Toda lattice is independent of the representation of sl(n,\({\mathbb{C}})\). It also generalizes a key result in the work of van Moerbeke and Mumford and makes it applicable to an arbitrary Lax pair. The periodic Toda lattice is treated in detail. The paper ends with a very detailed discussion of two curves associated to sl(4). It would be very interesting to extend these results to arbitrary semi-simple Lie algebras.
Reviewer: T.Ratiu
MSC:
| 37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 70H20 | Hamilton-Jacobi equations in mechanics |
| 35Q99 | Partial differential equations of mathematical physics and other areas of application |
Keywords:
integrable system; loop algebra; linearization procedure; periodic Toda lattice; semi-simple Lie algebrasReferences:
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