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A universal dimension formula for complex simple Lie algebras
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We present a universal formula for the dimension of the Cartan powers of the adjoint representation of a complex simple Lie algebra (i.e., a universal formula for the Hilbert functions of homogeneous complex contact manifolds), as well as several other universal formulas. These formulas generalize formulas of Vogel and Deligne and are given in terms of rational functions where both the numerator and denominator decompose into products of linear factors with integer coefficients. We also discuss some consequences of the formulas including a relation with Scorza varieties.
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Cited by 2 Pith papers
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Construction of Lie algebra weight system kernel via Vogel algebra
Using Vogel's Lambda algebra, the authors construct and explicitly list the first Jacobi diagrams in the kernel of the sl_n weight system, up to order 10 for primitive diagrams.
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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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