# Quasi-classical limit of Toda hierarchy andW-infinity symmetries

@article{Takasaki1993QuasiclassicalLO,
title={Quasi-classical limit of Toda hierarchy andW-infinity symmetries},
author={Kanehisa Takasaki and Takashi Takebe},
journal={Letters in Mathematical Physics},
year={1993},
volume={28},
pages={165-176}
}
• Published 18 January 1993
• Mathematics
• Letters in Mathematical Physics
Previous results on quasi-classical limit of the KP hierarchy and itsW-infinity symmetries are extended to the Toda hierarchy. The Planck constantħ now emerges as the spacing unit of difference operators in the Lax formalism. Basic notions, such as dressing operators, Baker-Akhiezer functions, and tau function, are redefined.W1 + ∞ symmetries of the Toda hierarchy are realized by suitable rescaling of the Date-Jimbo-Kashiara-Miwa vertex operators. These symmetries are contracted tow1…
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## References

SHOWING 1-10 OF 27 REFERENCES
Quasiclassical limit of KP hierarchy,W-symmetries, and free fermions
• Physics
• 1992
This paper deals with the dispersionless KP hierarchy from the point of view of quasiclassical limit. Its Lax formalism, W-infinity symmetries, and general solutions are shown to be reproduced from
SDiff(2) Toda equation — Hierarchy, Tau function, and symmetries
• Mathematics
• 1991
A continuum limit of the Toda lattice field theory, called the SDiff(2) Toda equation, is shown to have a Lax formalism and an infinite hierarchy of higher flows. The Lax formalism is very similar to
Hamiltonian formalism of Whitham-type hierarchies and topological Landau-Ginsburg models
We show that the bi-hamiltonian structure of the averaged Gelfand-Dikii hierarchy is involved in the Landau-Ginsburg topological models (forAn-Series): the Casimirs for the first P.B. give the
The structure of theW∞ algebra
We prove rigorously that the structure constants of the leading (highest spin) linear terms in the commutation relations of the conformal chiral operator algebraW∞ are identical to those of the
The dispersionless Lax equations and topological minimal models
It is shown that perturbed rings of the primary chiral fields of the topological minimal models coincide with some particular solutions of the dispersionless Lax equations. The exact formulae for the
Representation theoretical meaning of the initial value problem for the Toda lattice hierarchy: I
The Toda lattice hierarchy is shown to have the Bruhat decomposition of the A∞ group as its parameter space instead of the Grassmann manifold for the KP hierarchy. Takasaki's work on the initial
Solitons and Infinite Dimensional Lie Algebras
• Mathematics
• 1983
Introduction §1. Fock Representation of gf(°°) §2. T Functions and the KP Hierarchy §3. Reduction to A[" §4. Fermions with 2 Components §5. Algebras B^ and Co §6. Spin Representation of J&TO §7.