Partitions, vertex operator constructions and multi-component KP equations

M. J. Bergvelt, A. P.E. Ten Kroode

Research output: Contribution to journalArticlepeer-review


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 and hence a t function. We use these fundamental representations to study the Gauss decomposition in the infinite matrix group Gl and to express the Baker function in terms of t-functions. The reduction to loop algebras is discussed.

Original languageEnglish (US)
Pages (from-to)23-88
Number of pages66
JournalPacific Journal of Mathematics
Issue number1
StatePublished - Nov 1995

ASJC Scopus subject areas

  • General Mathematics


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