Projection operators for simple lie groups

The solution of many problems in nuclear theory and elementary particle physics amounts to decomposing the reducible representations of the symmetry groups of quantum mechanical systems into irreducible components. To carry out this decomposition, projection operators are needed. In the present paper we have constructed, for all simple compact Lie groups $G(l)$ of the rank $l$ (both classical and exceptional), operators which project the arbitrary vector with the weight $f=(f_1,f_2,\dots,f_l)$ onto the highest weight vector of the irreducible representation $D^{[f]}$ of the group $G(l)$. The projection operators are represented in the form of series composed of powers of the infinitesimal operators, which makes them convenient for the solution of particular problems concerning the decomposition of reducible representations into irreducible components. The structure of the projection operators is given for all simple compact Lie groups by similar formulas.