Invariants of Colored Links and a Property of the Clebsch-Gordan Coefficients of $U_q(g)$

Deguchi, Tetsuo; Ohtsuki, Tomotada

Invariants of Colored Links and a Property of the Clebsch-Gordan Coefficients of $U_q(g)$

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Description

We show that multivariable colored link invariants are derived from the roots of unity representations of $U_q(g)$. We propose a property of the Clebsch-Gordan coefficients of $U_q(g)$, which is important for defining the invariants of colored links. For $U_q(sl_2) we explicitly prove the property, and then construct invariants of colored links and colored ribbon graphs, which generalize the multivariable Alexander polynomial.
4 pages