Vogel's diagrammatic Lambda-algebra enables truly universal computations of Lie-theoretic quantities, demonstrated via multiple examples.
Casimir eigenvalues for universal Lie algebra
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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.
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Refined Chern-Simons theory universality is restricted to simply laced Lie groups, unlike the original which applies to all simple Lie groups.
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Diagrammatic technique for Vogel's universality
Vogel's diagrammatic Lambda-algebra enables truly universal computations of Lie-theoretic quantities, demonstrated via multiple examples.
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A note on universality in refined Chern-Simons theory
Refined Chern-Simons theory universality is restricted to simply laced Lie groups, unlike the original which applies to all simple Lie groups.