A. P. Isaev, S. O. Krivonos
Published 2021-06-08Version 1
We construct characteristic identities for the split (polarized) Casimir operators of the simple Lie algebras in adjoint representation. By means of these characteristic identities, for all simple Lie algebras we derive explicit formulae for invariant projectors onto irreducible subrepresentations in T^{\otimes 2} in the case when T is the adjoint representation. These projectors and characteristic identities are considered from the viewpoint of the universal description of the simple Lie algebras in terms of the Vogel parameters.
Comments: 13 pages. arXiv admin note: substantial text overlap with arXiv:2102.08258
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