Calculation Of Characters By Complete Sets Of Commutative Operators

Character is used to mark the non-equivalent irreducible representations in group representations. The calculation of characters of group representation is the basis of studying the irreducible representation of groups. Eigenfunction method is applied to calculate the characters of all kinds of groups.Based on extending a special group named the dihedral groups, this thesis finds a specific theory of simplifying the eigenfunction method. The study of the group representation character is switched to the study of the center of a group algebra and generators for the center of a group algebra. Calculation of traditional eigenfunction method is decreased by means of the basis theory of matrix, abstract algebra and group theory. In this way, the irreducible character of the group G is calculated more simply. The process of the calculation of group character is also introduced, which is the detail revelation of integrality and simplicity of this theory.