A universal dimension formula for complex simple Lie algebras

Details A universal dimension formula for complex simple Lie algebras A universal dimension formula for complex simple Lie algebras

2004-01-22

arxiv.org/abs/math/0401296v2

Mathematics

Representation Theory

To appear in Advances in Math

Scientific paper

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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