The W1+∞(gl s)-symmetries of the s-component KP hierarchy

DOI10.1063/1.531511zbMath0864.35096arXivhep-th/9411069OpenAlexW1771825722MaRDI QIDQ5284277

Johan W. van de Leur

Publication date: 15 June 1997

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9411069

zbMATH Keywords

vertex operatorstau-functionsToda lattice hierarchy\(s\)-component KP hierarchypseudodifferential operators on wave functions

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Infinite-dimensional Lie (super)algebras (17B65) Pseudodifferential and Fourier integral operators on manifolds (58J40) Invariance and symmetry properties for PDEs on manifolds (58J70)

Related Items (4)

The n-component KP hierarchy and representation theory ⋮ Algebra of pseudodifferential operators and symmetries of equations in the Kadomtsev–Petviashvili hierarchy ⋮ Representations of centrally-extended Lie algebras over differential operators and vertex algebras ⋮ \(\mathcal W\)-symmetry of the adelic Grassmannian

Cites Work

• Transformation groups for soliton equations. Euclidean Lie algebras and reduction of the KP hierarchy
• Basic representations of affine Lie algebras and dual resonance models
• Unitary representations of some infinite dimensional groups
• Bosonic and fermionic realizations of the affine algebra \(\widehat {gl_ n}\)
• Quasifinite highest weight modules over the Lie algebra of differential operators on the circle
• On additional symmetries of the KP hierarchy and Sato's Bäcklund transformation
• Lie algebras of differential operators, their central extensions, and W- algebras
• Additional symmetries for integrable equations and conformal algebra representation
• KdV type hierarchies, the string equation and \(W_{1+\infty}\) constraints
• A Lax representation for the vertex operator and the central extension
• Operator Approach to the Kadomtsev-Petviashvili Equation–Transformation Groups for Soliton Equations III–
• Spin and wedge representations of infinite-dimensional Lie algebras and groups

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