双参数变形多模玻色算符的代数结构及其应用(Ⅲ)

Algebraic Structure of Two-Parameter Deformed Multi-mode Bose Operators and Their Applications (Ⅲ)

构造了双参数变形多模玻色算符高次幂的本征态，发现它们构成完备Ｈｉｌｂｅｒｔ空间，另外，还给出了双参数变形量子代数ＳＬｑ，ｓ（３）的数学结构、玻色实现以及Ｓｌｑ，ｓ（２）的阶类张量算符，指出将ＳＬｑ，ｓ（３）的上述结果推广到多模情况是容易的。

The eigenstates of the higher power of the two-paranneter deformed multi-mode bose opcmtors are constructed. It is found that they form a complete Hilbert space Further more, the mathematical structure and the corresponding boson realization of the two-parameterr deformed quantum algebra SL, (3) are given, and the 1/ 2 ratk tensor-like operators of SLq.s(2) are also presented. It is pointed out that the results of SL(3) is easily generalized to a multi-mode case.