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

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dc.creatorIkeda, Takeshi
dc.creatorYamada, Hiro-Fumi
dc.date2002-02-05
dc.date.accessioned2026-07-07T05:33:53Z
dc.date.available2026-07-07T05:33:53Z
dc.descriptionA 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.
dc.description10 pages, no figure
dc.identifierhttps://arxiv.org/abs/nlin/0202011
dc.identifierhttp://arxiv.org/abs/nlin/0202011
dc.identifierLett.Math.Phys. 60 (2002) 147-156
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80163
dc.subjectExactly Solvable and Integrable Systems
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectRepresentation Theory
dc.titlePolynomial τ-functions of the NLS-Toda hierarchy and the Virasoro singular vectors
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