Induced representations of the two-parameter Jordanian quantum algebra |
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Authors: | V K Dobrev S G Mihov |
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Institution: | (1) School of Computing and Mathematics, University of Northumbria, Newcastle, UK;(2) Institute of Nuclear Research and Nuclear Energy, Sofia, Bulgaria |
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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
(sl(2)),
=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
(sl(2)).
Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June
2001.
Permanent address of V.K.D. |
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Keywords: | |
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