A universal dimension formula for complex simple Lie algebras
Representation Theory
2007-05-23 v2 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.math/0401296,
title = {A universal dimension formula for complex simple Lie algebras},
author = {J. M. Landsberg and L. Manivel},
journal= {arXiv preprint arXiv:math/0401296},
year = {2007}
}
Comments
To appear in Advances in Math