论文标题
使用Bazin身份的广义Schur函数决定因素
Generalized Schur function determinants using the Bazin identity
论文作者
论文摘要
在文献中，有几种用于Schur函数的决定性公式：Jacobi-Trudi公式，双重Jacobi-Trudi公式，Giambelli Formula，Lascoux-Pragacz公式和Hamel-Goulden公式，Hamel-Goulden公式，Hamel-Goulden公式在Hamel-goulden公式的位置。在本文中，我们使用Bazin在1851年证明的身份来得出涉及麦克唐纳（MacDonald）第9次变体Schur函数变体的确定性身份。作为一种应用，我们证明了莫拉莱斯，pak和panova猜想的阶乘Schur功能的决定性身份。我们还获得了包含JIN结果的Hamel-Goulden公式的概括，并证明了Hamel-Goulden定理及其概括的相反。
In the literature there are several determinant formulas for Schur functions: the Jacobi-Trudi formula, the dual Jacobi-Trudi formula, the Giambelli formula, the Lascoux-Pragacz formula, and the Hamel-Goulden formula, where the Hamel-Goulden formula implies the others. In this paper we use an identity proved by Bazin in 1851 to derive determinant identities involving Macdonald's 9th variation of Schur functions. As an application we prove a determinant identity for factorial Schur functions conjectured by Morales, Pak, and Panova. We also obtain a generalization of the Hamel-Goulden formula, which contains a result of Jin, and prove a converse of the Hamel-Goulden theorem and its generalization.
