Representations of sl(n,\({\mathbb{C}})\) and the Toda lattice
type: Item
instance of: scholarly article
title: Representations of sl(n,\({\mathbb{C}})\) and the Toda lattice
zbMATH Open document ID: 0645.58024
DOI: 10.1215/S0012-7094-88-05604-9
author: Andrew McDaniel
published in: Duke Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 70H20
Mathematics Subject Classification ID: 35Q99
zbMATH DE Number: 4052630
zbMATH Keywords: integrable system
zbMATH Keywords: loop algebra
zbMATH Keywords: linearization procedure
zbMATH Keywords: periodic Toda lattice
zbMATH Keywords: semi-simple Lie algebras
reviewed by: T. S. Ratiu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4052630