= Jones-Wenzl idempotent
{c}
{title2=$f_n$}
= Jones-Wenzl projector
{c}
{synonym}
The Jones-Wenzl <idempotent> has identity-diagram coefficient one, satisfies $f_n^2=f_n$, and annihilates each adjacent cap-cup generator on either side. With $\delta=-A^2-A^{-2}$ and $\Delta_0=1$, $\Delta_1=\delta$, $\Delta_n=\delta\Delta_{n-1}-\Delta_{n-2}$, it is constructed recursively by $f_n=F-(\Delta_{n-2}/\Delta_{n-1})Fe_{n-1}F$, where $F=f_{n-1}\otimes1$. The required denominators must be nonzero. Its closed bracket trace is $\Delta_n=(-1)^n[n+1]$.
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