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Partitions, Vertex Operator Constructions and Multi-component KP equations

M. J. Bergvelt·A. P. E. ten Kroode
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Abstract

For every partition of a positive integer $n$ in $k$ parts and every point of an infinite Grassmannian we obtain a solution of the $k$ component differential-difference KP hierarchy and a corresponding Baker function. A partition of $n$ also determines a vertex operator construction of the fundamental representations of the infinite matrix algebra $gl_\infty$ and hence a $τ$ function. We use these fundamental representations to study the Gauss decomposition in the infinite matrix group $Gl_\infty$ and to express the Baker function in terms of $τ$-functions. The reduction to loop algebras is discussed.

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M. J. Bergvelt, A. P. E. ten Kroode. 1992-12-15. Partitions, Vertex Operator Constructions and Multi-component KP equations. https://arxiv.org/abs/hep-th/9212087

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