Induced representations of the two-parameter Jordanian quantum algebra*)


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Abstract

We construct induced infinite-dimensional representations of the two-parameter quantum algebra Ug,h(gl(2)) which is in duality with the deformation GLg,h(2). The representations depend on two representation parameters, but split into one-parameter representations of a one-generator central subalgebra and the three-generator Jordanian quantum subalgebra Uĝ(sl(2)), ĝ = g + h. The representations of the latter can be mapped to representations in one complex variable, which give a new deformation of the standard one-parameter vector-field realization of sl(2). These infinite-dimensional representations are reducible for some values of the representation parameters, and then we obtain canonically the finite-dimensional representations of Uĝ(sl(2))

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