| Summary: | 碩士 === 淡江大學 === 物理研究所 === 81 === The quantum group is the q-deformation of Lie algebras. It
appears when one tries to solve the famous quantum Yang-Baxter
equation (QYBE) from different physical models. The
representations of the quantum group associated with its QYBE
are of central importance in these problems. In this letter ,by
introducing the q-deformation of the oscillator algebra (boson
algebra). We generalize the uaual oscillator realization method
to obtain explicit expressions for the representations of the
quantum group SU_q(2),SU_q(3), SU_q(1,1). The method can be
applied to the quantum group SU_q(n),SP_q(n) and also expected
to study quantum groups of any classical Lie algebra by further
generalizations.
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