Finite Dimensional Irreducible Representation Of Quantum Superalgebra U_q(sl(2, 1))

Lie superalgebras and their quantized enveloping superalgebras have lots of application both in theoretical physics and mathematical physics.For example,in the study of q-deformed supersymmetry theory,link invariants and so on.Thus it has sparked wide research interest in these field.A complete classification of finite-dimensional classical simple Lie superalgebras over field C has been given by Kac and Scheunert,the corresponding irreducible representations fall into two classes,named typical representations or atypical representations.Marcu studied the decomposition of tensor product of two irreducible representations of spl(2,1).In this thesis,the classification of finite-dimensional irreducible weight modules of U_q(sl(2,1)) for a generic element q is given and the structures of these modules are studied in detail.Furthermore,we consider the decomposition of tensor products of two irreducible representations of U_q(sl(2,1)),and the decomposition formulas of tensor products of two typical modules,a typical module and an atypical module,two atypical modules are abtained case by case.