Quantization of the semisimple Lie group

The representative matrix method (Jour. Math. Phys. 15, 1086, 1974) is applied to any semisimple Lie group, with a special choice of representative matrices, to obtain a special differential representation of the group. It is shown that this choise of coordinates can be utilized to quantize the group resulting in new uncertainty principles. The second order invariant equation is then regarded as an energy eigenvalue equation to be satisfied by the wave function representing a multiplet of particles. An example is given with the group SU(3), which is a theory of quantized charge and hypercharge proposed some 15 years ago. (orig.)