论文标题
$ w $ type运营商在Schur功能和Schur Q-intimes上的操作
Action of $W$-type operators on Schur functions and Schur Q-functions
论文作者
论文摘要
在本文中，我们研究了一系列的W型差异操作员，它们自然出现在KP和BKP层次结构的对称代数中。特别是，它们在W-constraints中包括所有满足字符串方程的较高KDV层次结构的tau函数。我们将为这些操作员在所有普通的Schur函数和Schur的Q-功能上的作用提供简单的统一公式。作为此类公式的应用，我们将为Alexandrov的猜想和Mironov-Morozov的公式提供新的简单证明，这些公式表达了Brézin-Gross-witten和Kontsevich-Witten-Witten-Witten Tau函数，分别用简单系数的线性组合。
In this paper, we investigate a series of W-type differential operators, which appear naturally in the symmetry algebras of KP and BKP hierarchies. In particular, they include all operators in the W-constraints for tau functions of higher KdV hierarchies which satisfy the string equation. We will give simple uniform formulas for actions of these operators on all ordinary Schur functions and Schur's Q-functions. As applications of such formulas, we will give new simple proofs for Alexandrov's conjecture and Mironov-Morozov's formula, which express the Brézin-Gross-Witten and Kontsevich-Witten tau-functions as linear combinations of Q-functions with simple coefficients respectively.
