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

Takeshi Ikeda, Hiro Fumi Yamada

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

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
Volume60
Issue number2
DOIs
Publication statusPublished - May 2002

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Singular Vectors
Polynomial function
hierarchies
polynomials
Young Diagram
Vertex Operators
Virasoro Algebra
Schur Functions
algebra
Eigenvector
operators
Algebra
Arbitrary
Operator
eigenvectors
apexes
diagrams
Hierarchy
Family

Keywords

  • Nonlinear Schrödinger equation
  • Schur functions
  • Virasoro algebra

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Polynomial τ-functions of the NLS-Toda hierarchy and the Virasoro singular vectors. / Ikeda, Takeshi; Yamada, Hiro Fumi.

In: Letters in Mathematical Physics, Vol. 60, No. 2, 05.2002, p. 147-156.

Research output: Contribution to journalArticle

Ikeda, Takeshi ; Yamada, Hiro Fumi. / Polynomial τ-functions of the NLS-Toda hierarchy and the Virasoro singular vectors. In: Letters in Mathematical Physics. 2002 ; Vol. 60, No. 2. pp. 147-156.
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