From the \(w_\infty\)-algebra to its central extension: a \(\tau\)-function approach

DOI10.1016/0375-9601(94)00306-AzbMath0925.58031OpenAlexW1530480102MaRDI QIDQ1337092

Takahiro Shiota, Pierre van Moerbeke, Mark Adler

Publication date: 28 October 1994

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0375-9601(94)00306-a

zbMATH Keywords

pseudodifferential operatorsKP-hierarchyvertex operator

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items

The structure of the Kac-Wang-Yan algebra, On additional symmetries of the KP hierarchy and Sato's Bäcklund transformation, \({\mathcal W}_{1+\infty}\) and \({\mathcal W}(gl_ N)\) with central charge \(N\), Eigenvalues of the string constraints for the Kadomtsev-Petviashvili hierarchy, On the constrained KP hierarchy, A Lax representation for the vertex operator and the central extension, Representation theory of the vertex algebra \(W_{1+\infty}\), Extensions and generalizations of lattice Gelfand-Dickey hierarchy, The gauge transformations of the constrained \(q\)-deformed modified KP hierarchy and their relations with the additional symmetries, Additional symmetries of the dispersionless cKP hierarchy, Multivariate hypergeometric functions as \(\tau\)-functions of Toda lattice and Kadomtsev-Petviashvili equation, Gauge Transformation for BC _r -KP Hierarchy and Its Compatibility with Additional Symmetry, Additional symmetries and string equations of the noncommutative B and C type KP hierarchies, The AKS theorem, A.C.I. systems and random matrix theory, The “ghost” symmetry of the BKP hierarchy, The super $\mathcal {W}_{1+\infty }$ algebra with integral central charge, The additional symmetries for the BTL and CTL hierarchies

Cites Work

• Infinite dimensional Grassmannian structure of two-dimensional quantum gravity
• On additional symmetries of the KP hierarchy and Sato's Bäcklund transformation
• Lectures on classical \(W\)-algebras
• A Lax representation for the vertex operator and the central extension
• Matrix integrals, Toda symmetries, Virasoro constraints, and orthogonal polynomials
• INTEGRABLE HIERARCHIES AND DISPERSIONLESS LIMIT
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