Abstract
We construct induced infinite-dimensional representations of the two-parameter quantum algebraUg,h(gl(2)) which is in duality with the deformationGLg,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 subalgebraU \(_{\tilde g} \) (sl(2)),\(\tilde g\) =g + h. The representations of the latter can be mapped to representations in one complex variable, which give anew deformation of the standard one-parameter vector-field realization ofsl(2). These infinite-dimensional representations are reducible for some values of the representation parameters, and then we obtain canonically the finite-dimensional representations ofU \({\tilde g}\) (sl(2)).
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Dobrev, V.K., Mihov, S.G. Induced representations of the two-parameter Jordanian quantum algebra. Czech J Phys 51, 1299–1305 (2001). https://doi.org/10.1023/A:1013361717983
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DOI: https://doi.org/10.1023/A:1013361717983