Polynomial τ - functions of the NLS - Toda hierarchy and the Virasoro singular vectors
نویسنده
چکیده
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.
منابع مشابه
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