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Advances in Mathematics 201, 2 (2006) 379-407

A universal dimension formula for complex simple Lie algebras

Joseph M. Landsberg 1, Laurent Manivel 2

(15/04/2006)

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.

1 :	Department of Mathematics, Texas A&M University (TAMU)
	Météo France
2 :	Institut Fourier (IF)
	CNRS : UMR5582 – Université Joseph Fourier - Grenoble I

Domaine

:

Mathématiques/Géométrie algébrique

Mots Clés : simple Lie algebra – adjoint representation – Hilbert function – Scorza variety

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Contributeur : Laurent Manivel <>

Soumis le : Mercredi 15 Octobre 2008, 10:48:43

Dernière modification le : Mercredi 15 Octobre 2008, 11:51:10