The A2 Invariant

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We compute the $A2$ (or quantum $sl(3)$) invariant using the normalization and formulas of [Khovanov], which in itself follows [Kuperberg]:

(For In[1] see Setup)

10_22

10_35

As an example, let us check that the knots 10_22 and 10_35 have the same Jones polynomial but different $A2$ invariants:

The $A2$ invariant attains values on the knots and links known to KnotTheory:

[Khovanov] ^  M. Khovanov, $sl(3)$ link homology I, arXiv:math.QA/0304375.

[Kuperberg] ^  G. Kuperberg, Spiders for rank 2 Lie algebras, Comm. Math. Phys. 180 (1996) 109-151, arXiv:q-alg/9712003.