Construction of cyclic representations of quantum algebras at q
p
=1 from their regular representations |
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| Authors: | Hong-Chen Fu Mo-Lin Ge |
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| Institution: | (1) Theoretical Physics Division, Nankai Institute of Mathematics, 300071 Tianjin, People's Republic of China;(2) Department of Physics, Northeast Normal University, 130024 Changchun, People's Republic of China;(3) Theoretical Physics Division, Nankai Institute of Mathematics, 300071 Tianjin, People's Republic of China |
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| 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.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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| Keywords: | 17B10 17B37 |
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