Journal of Lie Theory 17 (2007), No. 2, 263--281
Copyright Heldermann Verlag 2007
An Exposition of the sl(N,C)-Weight System
Fumikazu Nagasato
Dept. of Mathematics, Tokyo Institute of Technology, 2-12-1 Meguro-ku, Oh-okayama, Tokyo 152-8551, Japan
fukky@math.titech.ac.jp
Takashi Takamuki
Dept. of Mathematics, Tokyo Institute of Technology, 2-12-1 Meguro-ku, Oh-okayama, Tokyo 152-8551, Japan
We show substantial formulas of the sl(N, C)-weight system from a representation theoretical viewpoint. Although some of them can be essentially recovered by the universal sl(N, C)-weight system formulated by the first author in "A diagrammatic construction of the (sl(N, C), ρ)-weight system", Interdisciplinary Information Sciences 9 (2003) 43--51, they have more efficient descriptions than the ones recovered by the universal weight system in the sense that the dimension of the representation space of sl(N, C) used in this paper is taken to be minimal. In addition, in this paper, we also have the aim of making an exposition of the sl(N, C)-weight system: we show some elementary facts which are not easy to calculate concretely.
Keywords: Feynman diagram, Jacobi diagram, Kontsevich invariant, Lie algebra, quantum invariant, weight system.
MSC: 17B10, 57M27
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