# Jones-Wenzl Idempotents

Here are some of the Jones-Wenzl idempotents in the Temperley-Lieb algebras. The coefficients are computed using Scott Morrison’s formula and my library temperley_lieb_cat. The data files can be deserialised, though calculation through jw(n) should be fast enough for all the values below. The pdf files use the convention that a closed loop resolves to $$X$$.

$$\text{JW}_1$$ pdf data $$\text{JW}_2$$ pdf data $$\text{JW}_3$$ pdf data
$$\text{JW}_4$$ pdf data $$\text{JW}_5$$ pdf data $$\text{JW}_6$$ pdf data
$$\text{JW}_7$$ data $$\text{JW}_8$$ data $$\text{JW}_9$$ data

From $$\text{JW}_7$$ onwards, $$\LaTeX$$ refuses to compile the document and from around 10 onwards, the coefficients overflow signed 128-bit integers and I haven’t yet implemented larger number values.