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The Adelic Grassmannian and Exceptional Hermite Polynomials

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Abstract

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.

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  1. Department of Mathematics, College of Charleston, Charleston, SC, 29424, USA

    Alex Kasman

  2. Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, B3H 3J5, Canada

    Robert Milson

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  1. Alex Kasman
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  2. Robert Milson
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Correspondence to Alex Kasman.

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Kasman, A., Milson, R. The Adelic Grassmannian and Exceptional Hermite Polynomials. Math Phys Anal Geom 23, 40 (2020). https://doi.org/10.1007/s11040-020-09365-z

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