Notes for AKT-140303/0:35:03

Value of [math]\displaystyle{ W_{\mathfrak{g},R} }[/math] on [math]\displaystyle{ IHX }[/math].

Computation for [math]\displaystyle{ I }[/math]

[math]\displaystyle{ \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} }[/math]

Here [math]\displaystyle{ s }[/math] is a dummy variable and could be replace by [math]\displaystyle{ e^{\prime} }[/math]