I would like to evaluate the following summation of Clebsch-Gordan and Wigner 6-j symbols in closed form:

$$\sum_{l,m} C_{l_2,m_2,l_1,m_1}^{l,m} C_{\lambda_2,\mu_2,\lambda_1,\mu_1}^{l,m} \left\{ \begin{array}{ccc} l & l_2 & l_1 \\ n/2 & n/2 & n/2 \end{array}\right\} \left\{ \begin{array}{ccc} l & \lambda_2 & \lambda_1 \\ n/2 & n/2 & n/2 \end{array}\right\}$$

with $n \in \left[0,\infty\right)$, $l,l_1,l_2,\lambda_1,\lambda_2 \in \left[0,n\right]$, $m \in \left[-l,l\right]$, $m_1 \in \left[-l_1,l_1\right]$, $m_2 \in \left[-l_2,l_2\right]$, $\mu_1 \in \left[-\lambda_1,\lambda_1\right]$ and $\mu_2 \in \left[-\lambda_2,\lambda_2\right]$. All indices are integers and n must be also even.

I have been using Varshalovich's Book, but can't find any identities that have been useful to simplify this. I am hoping that the result is something like $\delta_{l_2,\lambda_2}\delta_{m_2,\mu_2}\delta_{l_1,\lambda_1}\delta_{m_1,\mu_1}$, but I'm not sure that that will be the case. Any ideas of how to evaluate this?

This post imported from StackExchange Physics at 2015-06-26 11:15 (UTC), posted by SE-user okj