论文标题
阶乘超对称偏斜舒尔函数和第九个变化确定性身份
Factorial supersymmetric skew Schur functions and ninth variation determinantal identities
论文作者
论文摘要
最近已证明Hamel和Goulden的决定性身份适用于基于图表的Skew Schur函数的第九个变体。在这里，我们将这种方法及其结果扩展到了超对称偏度舒尔函数的基于类似的图表的第九个变化。这些tableaux建立在从未填充和底漆数字的字母中获取的条目，并且可以以多种不同的方式订购，每种都会导致确定性身份。在第九变化的水平上，相应的确定性身份都是不同的，但是丢失了超对称的原始概念。结果表明，这可以在涉及双阶段参数序列的第六个变化水平上进行修复。此外，结果表明，所得的阶乘超对称偏斜函数独立于字母中未进行的和启动条目的顺序。
The determinantal identities of Hamel and Goulden have recently been shown to apply to a tableau-based ninth variation of skew Schur functions. Here we extend this approach and its results to the analogous tableau-based ninth variation of supersymmetric skew Schur functions. These tableaux are built on entries taken from an alphabet of unprimed and primed numbers and that may be ordered in a myriad of different ways, each leading to a determinantal identity. At the level of the ninth variation the corresponding determinantal identities are all distinct but the original notion of supersymmetry is lost. It is shown that this can be remedied at the level of the sixth variation involving a doubly infinite sequence of factorial parameters. Moreover it is shown that the resulting factorial supersymmetric skew Schur functions are independent of the ordering of the unprimed and primed entries in the alphabet.
