Publication:
Invariant Tensors Formulae via Chord Diagrams

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2005
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Springer
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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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D.Bar–Natan, On the Vassiliev Knot invariants, Topology,34 (1995),pp.423–475. D.Bar–Natan, Lie Algebras and The Four Colour Problem,Combinatorica, 17–1 (1997), pp. 43–52. S.V.Chmutov and A.N.Varchenko, Remarks on the Vassiliev Knot Invariants Coming from sl2, Topology, 36 (1997),pp.153–178. V.O.Manturov, The Bracket Semigroup of knots,Mathematical Notes,2000, vol.67,4, pp. 468-478. V.O.Manturov, Lectures on the Theory of Knots and Their Invariants, Moscow, URSS Publishing House, 2001 (in Russian). V.O.Manturov, Chord Diagrams and Invariant Tensors, Proceedings of the 1st Colloquium on Lie Theory and Applications, Vigo, Spain.
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