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New expressions for the invariant operators of the unitary groups
Teoretičeskaâ i matematičeskaâ fizika, Tome 29 (1976) no. 3, pp. 357-369 Cet article a éte moissonné depuis la source Math-Net.Ru

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The invariant operators (or Casimir operators) for the unitary groups $U(n)$ and $SU(n)$ are considered. The eigenvalues of these operators for an arbitrary irreducible representation are expanded with respect to standard power sums $S_k$ defined by Eq. (2.8). For the coefficients $\beta_p(\nu)$ of this expansion the expressions (3.9), (3,17), and (3.18) are obtained; they holed for arbitrary rank $n-1$ of the group and arbitrary order $p$ of the invariant operator. These expressions considerably simplify the calculation of the eigenvalues of the invariant operators (especially for large $p$), which is demonstrated by a number of examples. The connection between the operators (2.1) and (5.3), which correspond to different ways of contracting indices, is found. 
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     author = {V. S. Popov},
     title = {New expressions for the invariant operators of the unitary groups},
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}
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V. S. Popov. New expressions for the invariant operators of the unitary groups. Teoretičeskaâ i matematičeskaâ fizika, Tome 29 (1976) no. 3, pp. 357-369. http://geodesic.mathdoc.fr/item/TMF_1976_29_3_a6/

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