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TMF, 1997, Volume 113, Number 2, Pages 231–260 (Mi tmf1075)  

This article is cited in 6 scientific papers (total in 6 papers)

$P_\infty$ algebra of KP, free fermions and 2-cocycle in the Lie algebra of pseudodifferential operators

P. Winternitza, A. Yu. Orlovb

a Université de Montréal
b P. P. Shirshov institute of Oceanology of RAS

Abstract: The symmetry algebra $P_\infty=W_\infty\oplus H\oplus I_\infty$ of integrable systems is defined. As an example, the classical Sophus Lie point symmetries of all higher KP equations are obtained. It is shown that one (“positive”) half of the point symmetries belongs to the $W_\infty$ symmetries, while the other (“negative”) part belongs to the $I_\infty$ ones. The corresponding action on the tau-function is obtained for the positive part of the symmetries. The negative part can not be obtained from the free fermion algebra. A new embedding of the Virasoro algebra into $\operatorname{gl}(\infty)$ describes conformal transformations of the KP time variables. A free fermion algebra cocycle is described as a PDO Lie algebra cocycle.

DOI: https://doi.org/10.4213/tmf1075

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English version:
Theoretical and Mathematical Physics, 1997, 113:2, 1393–1417

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Received: 07.04.1997

Citation: P. Winternitz, A. Yu. Orlov, “$P_\infty$ algebra of KP, free fermions and 2-cocycle in the Lie algebra of pseudodifferential operators”, TMF, 113:2 (1997), 231–260; Theoret. and Math. Phys., 113:2 (1997), 1393–1417

Citation in format AMSBIB
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\jour Theoret. and Math. Phys.
\yr 1997
\vol 113
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\pages 1393--1417
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Yu. Orlov, D. M. Shcherbin, “Hypergeometric Solutions of Soliton Equations”, Theoret. and Math. Phys., 128:1 (2001), 906–926  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Orlov, AY, “Multivariate hypergeometric functions as tau-functions of Toda lattice and Kadomtsev-Petviashvili equation”, Physica D-Nonlinear Phenomena, 152 (2001), 51  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    3. Nissimov, E, “Symmetries of supersymmetric integrable hierarchies of KP type”, Journal of Mathematical Physics, 43:5 (2002), 2547  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    4. J. Harnad, A. Yu. Orlov, “Scalar Products of Symmetric Functions and Matrix Integrals”, Theoret. and Math. Phys., 137:3 (2003), 1676–1690  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. Bernal, J, “Soliton-like structures and the connection between the Bq and KP equations”, Chaos Solitons & Fractals, 17:5 (2003), 951  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    6. Orlov, AY, “Soliton theory, symmetric functions and matrix integrals”, Acta Applicandae Mathematicae, 86:1–2 (2005), 131  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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