Polynomial τ-functions of the NLS-Toda hierarchy and the Virasoro singular vectors

Takeshi Ikeda, Hiro Fumi Yamada

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


A family of polynomial τ-functions for the NLS-Toda hierarchy is constructed. The hierarchy is associated with the homogeneous vertex operator representation of the affine algebra g of type A(1)1. These τ-functions are given explicitly in terms of Schur functions that correspond to rectangular Young diagrams. It is shown that an arbitrary polynomial τ-function which is an eigenvector of d, the degree operator of g, is contained in the family. By the construction, any τ-function in the family becomes a Virasoro singular vector. This consideration gives rise to a simple proof of known results on the Fock representation of the Virasoro algebra with c = 1.

Original languageEnglish
Pages (from-to)147-156
Number of pages10
JournalLetters in Mathematical Physics
Issue number2
Publication statusPublished - May 2002


  • Nonlinear Schrödinger equation
  • Schur functions
  • Virasoro algebra

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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