Abstract
Cyclic representations of maximal dimension of the quantum algebra U q L associated with any finite-dimensional simple Lie algebra L are studied from its regular representation at q p=1, which is proved to be a quotient module of itself as a left module with respect to some submodules. The general theory is given after an instructive example U q sl(2) is studied. Another explicit example U q sl(3) is also presented.
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This work is supported in part by the National Natural Science Foundation of China. Author Fu is also supported by the Jilin Provincial Science and Technology Foundation of China
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Fu, HC., Ge, ML. Construction of cyclic representations of quantum algebras at q p=1 from their regular representations. Letters in Mathematical Physics 25, 277–286 (1992). https://doi.org/10.1007/BF00398400
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DOI: https://doi.org/10.1007/BF00398400