# Sanity check on spider web calculation

For fun I began reading an interesting online paper I found, Spiders for rank 2 Lie algebras, and on page $5$ we have the following calculation, akin to a tensor product expansion via bilinearity:

$\hskip 0.8in$

However, I believe the $21=6+6+9$ should just be a $12=6+6$, so that $9$ appears only once in the final result as the coefficient of the second web you see. What's going on?

(Also, help on more pertinent tags would be appreciated.)

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Do you propose a 'spider' tag? –  Isaac Solomon Nov 15 '12 at 6:01

Yes, you are right. I think the fact that $21=6+6+9$ is a coincidence; I think it is more likely that Prof. Kuperberg transposed the digits $1$ and $2$.