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Casimir eigenvalues for universal Lie algebra

By R. L. Mkrtchyan, A. N. Sergeev and A. P. Veselov

Abstract

For two different natural definitions of Casimir operators for simple Lie algebras we show that their eigenvalues in the adjoint representation can be expressed polynomially in the universal Vogel's parameters $\alpha, \beta, \gamma$ and give explicit formulae for the generating functions of these eigenvalues.Comment: Slightly revised versio

Topics: Mathematics - Representation Theory, 17Bxx
Year: 2012
DOI identifier: 10.1063/1.4757763
OAI identifier: oai:arXiv.org:1105.0115
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