= Jones-Wenzl partial trace
{c}
{title2=$\operatorname{ptr}(f_n)=(\Delta_n/\Delta_{n-1})f_{n-1}$}
Close the last strand of the projector recursion. Closing $f_{n-1}\otimes1$ gives $\delta f_{n-1}$, while closing its cap-cup correction gives $f_{n-1}$. The coefficient is $\delta-\Delta_{n-2}/\Delta_{n-1}=\Delta_n/\Delta_{n-1}$. Iteration proves $\operatorname{tr}(f_n)=\Delta_n$ and supplies the normalization needed to split the two <fusion of Jones-Wenzl colors> channels in $f_{n-1}\otimes1$.
Back to article page
