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Regular version of the site

Article

Casimir eigenvalues for universal Lie algebras

Journal of Mathematical Physics. 2012. Vol. 53. P. 102-106.
Sergeev A., Mkrtchayn R., Veselov A.

For two different natural definitions of Casimir operators for simple Lie algebras we show that their eigenvalues in the adjoint representation can be expressed polyno- mially in the universal Vogel’s parameters α, β, γ and give explicit formulae for the generating functions of these eigenvalues.