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arXiv · hep-th/9211009

A Quadratic Deformation of the Heisenberg-Weyl and Quantum Oscillator Enveloping Algebras

Jens UH Petersen
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Abstract

A new 2-parameter quadratic deformation of the quantum oscillator algebra and its 1-parameter deformed Heisenberg subalgebra are considered. An infinite dimensional Fock module representation is presented which at roots of unity contains null vectors and so is reducible to a finite dimensional representation. The cyclic, nilpotent and unitary representations are discussed. Witten's deformation of $sl_2$ and some deformed infinite dimensional algebras are constructed from the $1d$ Heisenberg algebra generators. The deformation of the centreless Virasoro algebra at roots of unity is mentioned. Finally the $SL_q(2)$ symmetry of the deformed Heisenberg algebra is explicitly constructed.

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Jens UH Petersen. 1992-11-25. A Quadratic Deformation of the Heisenberg-Weyl and Quantum Oscillator Enveloping Algebras. https://doi.org/10.1142/s0217751x93001399

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