Invariant tensors and Casimir operators for simple compact Lie groups

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Abstract
The Casimir operators of a Lie algebra are in one-to-one correspondence with the symmetric invariant tensors of the algebra. There is an infinite family of Casimir operators whose members are expressible in terms of a number of primitive Casimirs equal to the rank of the underlying group. A systematic derivation is presented of a complete set of identities expressing nonprimitive symmetric tensors in terms of primitive tensors. Several examples are given including an application to an exceptional Lie algebra.

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