Graphical Calculus on Representations of Quantum Lie Algebras
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Graphical Calculus on Representations of Quantum Lie Algebras

  • Author(s): Kim, Dongseok
  • et al.

Published Web Location

https://arxiv.org/pdf/math/0310143.pdf
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Abstract

We develop graphical calculation methods. Jones-Wenzl projectors for U_q(sl(2,C)) are very powerful tools to find not only invariants of links but also invariants of 3-manifolds. We find single clasp expansions of generalized Jones-Wenzl projectors for simple Lie algebras of rank 2. Trihedron coefficients of the representation theory for U_q(sl(2,C)) has significant meaning and it is called 3j symbols. Using single clasp expansions for U_q(sl(3,C)), we find some trihedron coefficients of the representation theory of U_q(sl(3,C)). We study representation theory for U_q(sl(4,C)). We conjecture a complete set of relations for U_q(sl(4,C)).

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