Vertex operators and \(\tau\)-functions. Transformation groups for soliton equations. II (Q793232)
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scientific article; zbMATH DE number 3855615
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Vertex operators and \(\tau\)-functions. Transformation groups for soliton equations. II |
scientific article; zbMATH DE number 3855615 |
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Vertex operators and \(\tau\)-functions. Transformation groups for soliton equations. II (English)
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1981
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[For part I see the article reviewed in Zbl 0538.35065 above.] The aim of the article is to study soliton-type equations such as the Korteweg-de Vries equation, the Boussinesq equation, the Kadomtsev-Petviashvili equation, etc. through their transformation groups. After recalling the construction of Lepowsky and Wilson the authors show that the space of \(\tau\)-functions for the KdV hierarchy is the orbit of the highest weight vector of this representation. They discuss the reason why the vertex operator forms a Lie algebra. The ``vertex operator'' for the KP hierarchy is introduced and it is shown that it forms the Lie algebra \(gl(\infty)\).
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soliton-type equations
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Korteweg-de Vries equation
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Boussinesq equation
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Kadomtsev-Petviashvili equation
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transformation groups
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\(\tau\)-functions
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vertex operator
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Lie algebra
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