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arXiv · 2202.03139

Free boson realization of the Dunkl intertwining operator in one dimension

Luc Vinet·Alexei Zhedanov
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Abstract

The operator that intertwines between the $\mathbb{Z}_2$ - Dunkl operator and the derivative is shown to have a realization in terms of the oscillator operators in one dimension. This observation rests on the fact that the Dunkl intertwining operator maps the Hermite polynomials on the generalized Hermite polynomials.

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Luc Vinet, Alexei Zhedanov. 2022-01-06. Free boson realization of the Dunkl intertwining operator in one dimension. https://doi.org/10.1142/s0129055x22500258

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