Many Boson Realizations of Universal Nonlinear $W_{\infty }$-Algebras

Abstract

An infinite number of free field realizations of the universal nonlinear ${\hat{W}}_{\infty }^{(N)}$ (${\hat{W}}_{1+\infty }^{(N)}$) algebras, which are identical to the KP Hamiltonian structures, are obtained in terms of $p$ plus $q$ scalars of different signatures with $p-q=N$. They are generalizations of the Miura transformation, and naturally give rise to the modified KP hierarchies via corresponding realizations of the latter. Their characteristic Lie-algebraic origin is shown to be the graded $SL(p,q)$.

arXiv comment10p, (plain LaTex), Modified KP Hierarchies and Graded Lie Algebras

References in corpus (2)

• Nonlinear ${\hat{W}}_{\infty }$ Current Algebra in the SL(2,R)/U(1) Coset Model
• An Infinite Number of Commuting Quantum ${\hat{W}}_{\infty }$ Charges in the $SL(2,R)/U(1)$ Coset Model

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• The Constrained KP Hierarchy and the Generalised Miura Transformation
• Two-Matrix String Model as Constrained (2+1)-Dimensional Integrable System
• On the structure of graded Lie superalgebras
• Symmetries of Supersymmetric Integrable Hierarchies of KP Type
• The constrained modified KP hierarchy and the generalized Miura transformations
• On the Miura and Backlund transformations associated with the supersymmetric Gelfand-Dickey bracket
• Nonlocal extended conformal algebras associated with multi-constraint KP hierarchy and their free-field realizations
• Matrix Formulation of Hamiltonian Structures of Constrained KP Hierarchy
• V-Algebras and Their Free Field Realizations