Invariant Tensors Formulae via Chord Diagrams

2005/05/16 by R. Campoamor-Stursberg, V. O. Manturov
Mathematics · #math.GT #msc:57M25

paper · pdf

published as J. Math. Sci. 128 (2005), 3018-3029. · 18 pages, 8 figures. To appear in a special issue of Journal of Mathematical Sciences

arxiv created 2005/05/16 · arxiv updated 2009/12/01

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).

Related

• Tensor invariants of SL(n), wave graphs and L-tris
• Invariant Adjoint Tensors of the Classical Groups
• Euler's difference table and decomposition of tensor powers of adjoint representation of A_n Lie algebra
• Diagrams of representations
• Invariant tensors for simple groups