Notes for AKT-140303/0:35:03

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Value of W_{\mathfrak{g},R} on IHX.

Computation for I


\begin{align}
W_{\mathfrak{g},R}(I) & = f_{ecd}f_{abe^{\prime}}t^{ee^{\prime}} \\
& =  \langle[X_e, X_c], X_d \rangle \langle[X_a, X_b], X_e^{\prime} \rangle t^{ee^{\prime}} = f_{ec}^st_{sd} f_{ab}^kt_{ke^{\prime}}t^{ee^{\prime}}\\
& = f_{ec}^st_{sd} f_{ab}^k \delta_{k}^{e} \\
& = f_{ec}^sf_{ab}^et_{sd} 
\end{align}

Here s is a dummy variable and could be replace by e^{\prime}