A Quadratic Deformation of the Heisenberg-Weyl and Quantum Oscillator Enveloping Algebras
نویسنده
چکیده
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 sl2 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 SLq(2) symmetry of the deformed Heisenberg algebra is explicitly constructed. ◦ e-mail: [email protected] (decnet: 19678::petersen) Work supported by a S.E.R.C. Research Studentship
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