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

Latest revision as of 14:25, 18 July 2018

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

Computation for $I$

{\begin{aligned}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}^{s}t_{sd}f_{ab}^{k}t_{ke^{\prime }}t^{ee^{\prime }}\\&=f_{ec}^{s}t_{sd}f_{ab}^{k}\delta _{k}^{e}\\&=f_{ec}^{s}f_{ab}^{e}t_{sd}\end{aligned}}

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

@@ Line 1: / Line 1: @@
-'''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}
-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 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></center>
+Here <math>s</math> is a dummy variable and could be replace by <math>e^{\prime}</math>
-\end{align}</math></center>