C_λ-extended oscillator algebra and parasupersymmetric quantum mechanics

1998/08/20 by C. Quesne, N. Vansteenkiste
Mathematics · #math.QA

paper · pdf

published as Czech. J. Phys. 48 (1998) 1477-1482 · 7 pages, LaTeX, no figures, submitted to 7th Int. Coll. ``Quantum Groups and Integrable Systems'', Prague, 18-20 June 1998 (to be published in Czech. J. Phys.)

arxiv created 1998/08/20 · arxiv updated 2009/11/30

Abstract

The C_λ-extended oscillator algebra is generated by 1,a,a^†,N,T, where T is the generator of the cyclic group C_λ of order λ. It can be realized as a generalized deformed oscillator algebra (GDOA). Its unirreps can thus be exhibited using the representation theory of GDOAs and their carrier space show a Z_λ grading structure. Within its infinite-dimensional Fock space representation, this algebra provides a bosonization of parasupersymmetric quantum mechanics of order p= λ- 1.

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