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.

中文翻译：

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Adelic Grassmannian 和异常 Hermite 多项式

结果表明，当添加对 KP 层次结构的第二个流的依赖时，乔治·威尔逊 (George Wilson) 的阿德利格拉斯曼 (adelic Grassmannian) 中某些点的半平稳波函数是例外 Hermite 正交多项式的生成函数。不同数学对象之间的这种令人惊讶的对应关系，以前不知道如此密切相关，这本身就很有趣，但也证明在两个方面很有用：它导致了有效计算相关微分和差分算子的新算法，它也回答了关于他们的一些开放性问题。