Representation theoretical meaning of the initial value problem for the Toda lattice hierarchy. II
type: Item
instance of: scholarly article
title: Representation theoretical meaning of the initial value problem for the Toda lattice hierarchy. II
zbMATH Open document ID: 0785.35106
author: Takashi Takebe
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1992-09-26T00:00:00Z
review text: The Toda lattice hierarchy is shown to have the virtual Bruhat decomposition of the \(A_ \infty\) group as its parameter space, instead of the Grassmann manifold for the KP hierarchy. The open cell of this Bruhat decomposition was examined in the first part of this series [Lett. Math. Phys. 21, No. 1, 77-84 (1991; Zbl 0733.35098)]. In the present paper, based on the above work, a one-to-one correspondence between points in the small cells and pseudo-regular solutions is established.
Mathematics Subject Classification ID: 35Q58
Mathematics Subject Classification ID: 81R10
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 82C23
Mathematics Subject Classification ID: 81T40
zbMATH DE Number: 55945
zbMATH Keywords: Miura transformation
zbMATH Keywords: Toda lattice hierarchy
zbMATH Keywords: Bruhat decomposition
zbMATH Keywords: small cells
zbMATH Keywords: pseudo-regular solutions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195169665
OpenAlex ID: W2026525976
cites work: Q3688825
cites work: Solitons and infinite dimensional Lie algebras
cites work: Geometric realization of conformal field theory on Riemann surfaces
cites work: Q3327361
cites work: Q3697940
cites work: Representation theoretical meaning of the initial value problem for the Toda lattices hierarchy. I
DOI: 10.2977/PRIMS/1195169665
description: scientific article; zbMATH DE number 55945