A universal dimension formula for complex simple Lie algebras Academic Article uri icon


  • 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 discuss consequences of the formulas including a relation with Scorza varieties. 2005 Elsevier Inc. All rights reserved.

published proceedings

  • Advances in Mathematics

author list (cited authors)

  • Landsberg, J. M., & Manivel, L.

citation count

  • 32

complete list of authors

  • Landsberg, JM||Manivel, L

publication date

  • April 2006