Polynomial τ-Functions of the NLS-Toda Hierarchy and the Virasoro Singular Vectors
Polynomial τ-Functions of the NLS-Toda Hierarchy and the Virasoro Singular Vectors
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NLS-Toda 层次结构和 Virasoro 奇异向量的多项式 τ 函数
DOI：
10.1023/a:1016167008456
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发表时间：
2002
影响因子：
1.2
通讯作者：
Hirofumi Yamada
中科院分区：
文献类型：
--
作者：
T. Ikeda;Hirofumi Yamada
本文构造了NLS-Toda族的多项式τ-函数族。该层次与仿射代数的齐次顶点算子表示相关联
$$\mathfrak{g}$$
类型A1（1）。这些τ-函数以Schur函数的形式给出，Schur函数对应于矩形Young图。证明了任意多项式τ-函数是d的特征向量，
$$\mathfrak{g}$$
它包含在家庭中。通过构造，族中的任意τ-函数都成为Virasoro奇异向量.这一考虑引起了一个简单的证明已知的结果Fock表示的Virasoro代数与c = 1。
AbstractA 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
$$\mathfrak{g}$$
of type A1(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
$$\mathfrak{g}$$
, 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.