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Graphical Calculus on Representations of Quantum Lie Algebras

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arxiv math/0310143 v1 pith:QBGWMZLS submitted 2003-10-10 math.QA math.RT

Dongseok Kim This is my paper · ORCID
classification math.QAmath.RT
keywords findrepresentationtheoryalgebrasclaspcoefficientsexpansionsgraphical
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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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Cited by 1 Pith paper

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  1. Web Diagrams of Cluster Variables for Grassmannian Gr(4,8)

    math.CO 2025-07 conditional novelty 5.0 of 10

    This paper gives explicit web diagrams and dual webs for quadratic and cubic cluster variables in C[Gr(4,8)].

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