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

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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.
10 pages, no figure

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Exactly Solvable and Integrable Systems, High Energy Physics - Theory, Mathematical Physics, Representation Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/80163

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/nlin/0202011
 http://arxiv.org/abs/nlin/0202011
 Lett.Math.Phys. 60 (2002) 147-156

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arXiv