2004/01/22 by J. M. Landsberg, Landsberg, J. M., Laurent Manivel +2 · 6 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #math.AG #math.RT
paper · pdf · doi:10.48550/arxiv.math/0401296
To appear in Advances in Math
openalex publication_date 2004/01/22 · arxiv created 2005/02/01 · arxiv updated 2009/12/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
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.