Invariant Tensors Formulae via Chord Diagrams

Abstract

We provide an explicit algorithm to calculate invariant tensors for the adjoint representation of the simple Lie algebra $sl(n)$, as well as arbitrary representation in terms of roots. We also obtain explicit formulae for the adjoint representations of the orthogonal and symplectic Lie algebras $so(n)$ and $sp(n)$.

18 pages, 8 figures. To appear in a special issue of Journal of Mathematical Sciences