| Abstract: |
| The exceptional Hermite orthogonal polynomials are a generalization of the classical Hermite polynomials that are of interest to researchers in approximation theory and in quantum mechanics. Since they are an instance of differential/difference bispectrality in rank two, one might expect that a suitable generalization of Wilson`s methods for differential/differential rank one bispectrality would be required to study them. Surprisingly, we found that no generalization was needed at all. The exceptional Hermites were hiding in Wilson`s adelic Grassmannian all along. They can be seen if you retain not just one of the time variables of the KP hierarchy (as did Wilson) but \textit{two} of them. This correspondence is useful since it provides new effective methods for producing the polynomials and their associated operators and also because it answers some open questions about them. |
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