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Free boson realization of the Dunkl intertwining operator in one dimension (2202.03139v1)
Published 6 Jan 2022 in math.CA, math-ph, and math.MP
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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