A universal dimension formula for complex simple Lie algebras Academic Article

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

authors

• Landsberg, Joseph

published proceedings

• ADVANCES IN MATHEMATICS

author list (cited authors)

• Landsberg, J. M., & Manivel, L.

citation count

• 35

complete list of authors

• Landsberg, JM||Manivel, L

publication date

• January 2006

publisher

• Elsevier  Publisher

published in

• Advances in Mathematics  Journal

keywords

• Homogeneous Complex Contact Manifold
• Scorza Variety
• Universal Lie Algebra

Digital Object Identifier (DOI)

• 10.1016/j.aim.2005.02.007

start page

• 379

end page

• 407

volume

• 201

issue

• 2

URL

• http://dx.doi.org/10.1016/j.aim.2005.02.007