ON A CLASS OF NONSTANDARD QUANTUM ALGEBRAS AND THEIR REPRESENTATIONS*)


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Abstract

The nonstandard Uzsl(2,Symbol 1) quantum algebra is considered together with other non-standard algebras sharing the same universal R-matrix as well as a fixed Hopf subalgebra. Some boson realizations for these nonstandard algebras are obtained which are later used in order to compute in a simplified way their (finite and infinite dimensional) representations. In the limit when the deformation parameter z vanishes these realizations turn into the well known (one or two-boson) Gelfand-Dyson realizations for the corresponding classical Lie algebras.

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