General charge conjugation operators in simple Lie groups

Abstract

A description of particular elements ("charge conjugation operators") found in any compact simple Lie group K is presented. Such elements Ri transform a physical state (weight vector of a basis of a representation space) into others with opposite "charge" (ith component of the weight), sometime changing also the sign of the state. It is demonstrated that exploitation of these elements and the finite subgroup N of K generated by them offer new powerful methods for computing with representations of the Lie group. Their application to construction of bases in representation spaces is considered in detail. It represents a completely new direction to the problem.