Free boson realization of the Dunkl intertwining operator in one dimension

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.

10 pages. Dedicated to the memory of Jiři Patera

References in corpus (1)

• Free Oscillator Realization of the Laguerre Polynomial

Cited by in corpus (3)

• Ideal Bose Gas and Blackbody Radiation in the Dunkl Formalism
• The condensation of ideal Bose gas in a gravitational field in the framework of Dunkl-statistic
• Rationally-extended Dunkl oscillator on the line