Invariant Tensors Formulae via Chord Diagrams

Details Invariant Tensors Formulae via Chord Diagrams Invariant Tensors Formulae via Chord Diagrams

2005-05-16

arxiv.org/abs/math/0505320v1

J. Math. Sci. 128 (2005), 3018-3029.

Mathematics

Geometric Topology

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

Scientific paper

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 $sp(n)$.

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