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

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

1992-11-02

arxiv.org/abs/hep-th/9211009v2

Int.J.Mod.Phys. A8 (1993) 3479-3494

Physics

High Energy Physics

High Energy Physics - Theory

23 pages of plain TeX (with phyzzx.tex macros). I've made a few minor corrections and added 2 references

Scientific paper

10.1142/S0217751X93001399

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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