标题： 与超对称八顶点模型相关的特殊多项式：总结 显示英文标题

标题： Special polynomials related to the supersymmetric eight-vertex model: A summary

摘要： 我们引入并研究对称多项式，这些多项式作为特例包括与超对称八顶点模型相关的多项式，以及其他具有$\Delta=\pm 1/2$的椭圆格点模型。 还与仿射李代数特征有密切关系。 在进行自然变量替换后，我们的多项式满足带有椭圆势的非稳态薛定谔方程，这与Knizhnik-Zamolodchikov-Bernard方程以及Painlevé VI的规范量子化有关。 此外，我们多项式的特殊形式可以与从Picard的一个代数解通过四维格点的Bäcklund变换作用得到的Painlevé VI的tau函数相识别。 在本工作中，我们对这些主题的结果进行了总结，仅包含最少的技术细节。 显示英文摘要

摘要： We introduce and study symmetric polynomials, which as very special cases include polynomials related to the supersymmetric eight-vertex model, and other elliptic lattice models with $\Delta=\pm 1/2$. There is also a close relation to affine Lie algebra characters. After a natural change of variables, our polynomials satisfy a non-stationary Schr\"odinger equation with elliptic potential, which is related to the Knizhnik-Zamolodchikov-Bernard equation and to the canonical quantization of Painlev\'e VI. Moreover, specializations of our polynomials can be identified with tau functions of Painlev\'e VI, obtained from one of Picard's algebraic solutions by acting with a four-dimensional lattice of B\"acklund transformations. In the present work, our results on these topics are summarized with a minimum of technical details.