论文标题
对量子仿射Kz方程和麦克唐纳型特征值问题的等级一双光对应关系的评论
A review of rank one bispectral correspondence of quantum affine KZ equations and Macdonald-type eigenvalue problems
论文作者
论文摘要
该注释由两个部分组成。第一部分（第1和§2）是对Van Meer和Stokman（2010），Van Meer（2011）和Stokman（2014）的作品的部分综述，该作品建立了Cherednik对应关系的双光谱类似物，量子对应于量子量，knizhik-Zamolodchikov方程与Macdonald类型的eigenvalue问题。在这篇综述中，我们将重点放在排名第一的情况下，即减少的类型$ A_1 $和非还原类型的$（C_1^\ vee，C_1）$，相关的MacDonald-Koornwinder是Rogers多项式的，Rogers是多项式的，分别是Askeyskey-Wilson-Wilson polynomials。我们提供了在文献中可能难以找到的详细计算和公式。 The second part (§3) is a complement of the first part, and is also a continuation of our previous study (Y.-Y., 2022) on the parameter specialization of Macdonald-Koornwinder polynomials, where we found four types of specialization of the type $(C_1^\vee,C_1)$ parameters (which could be called the Askey-Wilson parameters) to recover the type $A_1$.在本说明中，我们表明，在四个专业中，只有一个与第一部分中讨论的双光谱对应关系兼容。
This note consists of two parts. The first part (§1 and §2) is a partial review of the works by van Meer and Stokman (2010), van Meer (2011) and Stokman (2014) which established a bispectral analogue of the Cherednik correspondence between quantum affine Knizhnik-Zamolodchikov equations and the eigenvalue problems of Macdonald type. In this review we focus on the rank one cases, i.e., on the reduced type $A_1$ and the non-reduced type $(C_1^\vee,C_1)$, to which the associated Macdonald-Koornwinder polynomials are the Rogers polynomials and the Askey-Wilson polynomials, respectively. We give detailed computations and formulas that may be difficult to find in the literature. The second part (§3) is a complement of the first part, and is also a continuation of our previous study (Y.-Y., 2022) on the parameter specialization of Macdonald-Koornwinder polynomials, where we found four types of specialization of the type $(C_1^\vee,C_1)$ parameters (which could be called the Askey-Wilson parameters) to recover the type $A_1$. In this note, we show that among the four specializations there is only one which is compatible with the bispectral correspondence discussed in the first part.
