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Free boson realization of the Dunkl intertwining operator in one dimension

Centre de Recherches Mathématiques, Université de Montréal, P. O. Box 6128, Centre-ville Station, Montréal, Québec, H3C 3J7, Canada

Institut de Valorisation des Données (IVADO), Montréal, Québec, H2S 3H1, Canada

E-mail Address: vinet@crm.umontreal.ca

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and

Alexei Zhedanov

School of Mathematics, Renmin University of China, Beijing 100872, P. R. China

E-mail Address: zhedanov@yahoo.com

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https://doi.org/10.1142/S0129055X22500258Cited by:3 (Source: Crossref)

Abstract

The operator that intertwines between the $ℤ_{2}$ -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.

Dedicated to the memory of Jiři Patera

Keywords:

AMSC: 81Q80, 33C45

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