Sp(4)群和SO(5)群的C-G级数

C—G SERIES OF Sp (4) AND SO (5) GROUPS

本文从Littlewood给出的公式出发,利用Schur函数运算规则及Sp(4)群不可约表示的修正规则,得到了确定Sp(4)群C—G级数的普遍公式。考虑到SO(5)群和Sp(4)群局部同构,利用其不可约表示间的对应关系,给出了确定SO(5)群C—G级数的普遍公式。

In this paper, starting from the formula given by Littlewood, the general formula which can be used to determine the C—G series of Sp(4) group is obtained in compliance with operation rule of schur function and modification rule for irreducible representation of Sp(4). Taking local isomorphism between SO(5) and Sp(4) into account) the general formula for determining the C—G series of SO(5) group is given with the aid of the correspondence between irreducible repro—sentation of SO(5) and that of Sp(4).