【摘要】 在有限群中引入一个完备算符,它具有李群中决定不可约表示的Casimir不变算符集同样的作用,完全决定有限群的不可约表示,所有类算符都能表示为完备算符的多项式函数,并且完备算符自己满足K(类数)次代数方程,由此来决定完备算符的K个不同本征值,随之也就确定了所有类算符的本征值。根据类算符本征值与特征标的关系,就能直接求出所有的特征标,完全确定有限群的所有不可约表示,最后得出各种有限群均为一秩群的结论。更多还原

【Abstract】 To find the irreducible representations of finite group, we have introduced a complete operator which determines the irreducible representations of the finite group completely. The role that operator has played is just like that played by the set of Casimir invariant operator in the determination of the irreducible representations of Lie group. The class operators can all be represented in the polynomial functions of the complete operator which satisfies an algebraic equation in K-th degree itself, and its K eigenvalues are determined by the equation, and the eigenvalues of all the class operators are thus detemined By the relation between the eigenvalues of the class operator and its characters, we can find these characters as soon as the irreducible representations of the finite group are determined. The results we got is that various finite groups are allin the first rank.更多还原