论文标题
Hall-Littlewood多项式的顶点操作员的线性转换
Linear transformations of vertex operator presentations of Hall-Littlewood polynomials
论文作者
论文摘要
我们研究了线性转化对量子场的影响，并应用了对称函数的顶点操作员的应用。描述了线性转化的量子场的特性和Hall-Littlewood多项式的相应转换，包括保留换向关系，稳定性，显式组合公式和生成功能。我们证明，线性转化的霍尔 - 小木多项式的专长描述了KP和BKP层次结构的所有多项式tau函数。线性转换的示例与多参数对称函数，Grothendieck多项式，环形多项式变形以及文献中存在的Schur对称函数的其他一些变化有关。
We study the effect of linear transformations on quantum fields with applications to vertex operator presentations of symmetric functions. Properties of linearly transformed quantum fields and corresponding transformations of Hall-Littlewood polynomials are described, including preservation of commutation relations, stability, explicit combinatorial formulas and generating functions. We prove that specializations of linearly transformed Hall-Littlewood polynomials describe all polynomial tau functions of the KP and the BKP hierarchy. Examples of linear transformations are related to multiparameter symmetric functions, Grothendieck polynomials, deformations by cyclotomic polynomials, and some other variations of Schur symmetric functions that exist in the literature.
