New formulas for invariant operators of unitary groups

Invariant operators (Casimir operators) for unitary groups U(n) and SU(n) are considered. The eigenvalues of these operators for arbitrary irreducible representation are expanded in the standard power sums Ssub(k). For the coefficients βsub( )(ν) of this expansion, the formulas are obtained which are valid for arbitrary values of the rank n - I of the group and the order p of the invariant operator. These formulas simplify the calculation of the eigenvalues of invariant operators considerably (especially for large values of p), which is demonstrated by a number of examples. Connection between the operators corresponding to different ways of convolution of indices, is found