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Funktsional'nyi Analiz i ego Prilozheniya, 1999, Volume 33, Issue 4, Pages 1–24
DOI: https://doi.org/10.4213/faa377
(Mi faa377)
 

Intertwining Operators and Soliton Equations

M. I. Golenishcheva-Kutuzovaa, D. R. Lebedevb

a Landau Institute for Theoretical Physics, Centre for Non-linear Studies
b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
References:
Abstract: The fermionic approach to the Kadomtsev–Petviashvili hierarchy, suggested by the Kyoto school (Sato, Date, Jimbo, Kashiwara, and Miwa) in 1981–4, is generalized on the basis of the idea that, in a sense, the components of intertwining operators are a generalization of free fermions for $gl_\infty$. Integrable hierarchies related to symmetries of Kac–Moody algebras are described in terms of intertwining operators. The bosonization of these operators for various choices of the Heisenberg subalgebra is explicitly written out. These various realizations result in distinct hierarchies of soliton equations. For example, for $sl_N$-symmetries this gives the hierarchies obtained by the $(n_1,\dots,n_s)$-reduction from the $s$-component KP hierarchy introduced by Kac and van de Leur.
Received: 16.09.1998
English version:
Functional Analysis and Its Applications, 1999, Volume 33, Issue 4, Pages 241–259
DOI: https://doi.org/10.1007/BF02467108
Bibliographic databases:
Document Type: Article
UDC: 512.8+517.95
Language: Russian
Citation: M. I. Golenishcheva-Kutuzova, D. R. Lebedev, “Intertwining Operators and Soliton Equations”, Funktsional. Anal. i Prilozhen., 33:4 (1999), 1–24; Funct. Anal. Appl., 33:4 (1999), 241–259
Citation in format AMSBIB
\Bibitem{GolLeb99}
\by M.~I.~Golenishcheva-Kutuzova, D.~R.~Lebedev
\paper Intertwining Operators and Soliton Equations
\jour Funktsional. Anal. i Prilozhen.
\yr 1999
\vol 33
\issue 4
\pages 1--24
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\crossref{https://doi.org/10.4213/faa377}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1746426}
\zmath{https://zbmath.org/?q=an:1073.37540}
\transl
\jour Funct. Anal. Appl.
\yr 1999
\vol 33
\issue 4
\pages 241--259
\crossref{https://doi.org/10.1007/BF02467108}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000086100900001}
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