C_λ-extended oscillator algebra and parasupersymmetric quantum mechanics
Abstract
Description
The C_λ-extended oscillator algebra is generated by {1,a,a^{\dagger},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.
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.)
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.)