Notes for AKT-140303/0:35:03: Difference between revisions

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'''Value of <math>W_{\mathfrak{g},R}</math> on <math>\mathcal{IHX}</math>'''.
'''Value of <math>W_{\mathfrak{g},R}</math> on <math>IHX</math>'''.


Computation for <math>\mathcal{I}</math>
Computation for <math>I</math>




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

Revision as of 11:22, 12 July 2018

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 = 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]
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