论文标题
Adelic Grassmannian和非凡的Hermite多项式
The Adelic Grassmannian and Exceptional Hermite Polynomials
论文作者
论文摘要
结果表明，当添加依赖KP层次结构的第二个流动时，乔治·威尔逊（George Wilson）的Adelic Grassmannian中某些点的某些点的半平稳波函数正在产生异常的Hermite正交多项式的功能。以前未知的不同数学对象之间的这种令人惊讶的对应关系本身就是有趣的，但也以两种方式证明：它导致了有效计算相关的差异和差异操作员的新算法，并且还回答了一些关于它们的开放问题。
It is shown that when dependence on the second flow of the KP hierarchy is added, the resulting semi-stationary wave function of certain points in George Wilson's adelic Grassmannian are generating functions of the exceptional Hermite orthogonal polynomials. This surprising correspondence between different mathematical objects that were not previously known to be so closely related is interesting in its own right, but also proves useful in two ways: it leads to new algorithms for effectively computing the associated differential and difference operators and it also answers some open questions about them.
