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Fock Spaces for the Complex Dunkl Operator and Deformed (1, 1) Algebra

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In this paper, we study a class of generalized Fock spaces for the complex Dunkl operator associated with the cyclic group, generalizing the Bargmann representations for Lie algebra su(1,1)-generators. We present an explicit realization of Cr-extended oscillator in terms of this operator. Furthermore, we construct the wave functions and we determine the coherent states. We also determine an explicit realization of a polynomial deformation sud(1,1) of the classical Lie algebra su(1,1). Finally, we give a deforming functional which maps sud(1,1) to su(1,1).

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  1. Department of Mathematics, Faculty of Sciences of Tunis, University El Manar, 2092, Tunis, Tunisia

    Kamel Mezlini

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  1. Kamel Mezlini
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Correspondence to Kamel Mezlini.

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Mezlini, K. Fock Spaces for the Complex Dunkl Operator and Deformed (1, 1) Algebra. Int J Theor Phys 59, 2509–2528 (2020). https://doi.org/10.1007/s10773-020-04518-w

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  • DOI: https://doi.org/10.1007/s10773-020-04518-w

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