Theoretical and Mathematical Physics

, Volume 104, Issue 1, pp 783–792 | Cite as

The [n1,n2, ...,ns]-th reduced KP hierarchy andW1+∞ constraints

  • J. van de Leur


To every partition n=n1+n2+...+ns one can associate a vertex operator realization of the Lie algebras a and gln. Using this construction, we obtain reductions of the s-component KP hierarchy, reductions which are related to these partitions. In this way we obtain matrix KdV-type equations. We show that the following two constraints on a KP τ-function are equivalent: (1) τ is a τ-function of the [n1, n2, ..., ns]-th reduced KP hierarchy which satisfies the string equation L−1τ=0; (2) τ satisfies the vacuum constraints of the W1+∞ algebra.


Vertex Operator Operator Realization String Equation Vacuum Constraint Vertex Operator Realization 
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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • J. van de Leur
    • 1
  1. 1.UtrechtThe Netherlands

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