The A2 Invariant

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We compute the [math]\displaystyle{ A2 }[/math] (or quantum [math]\displaystyle{ sl(3) }[/math]) 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 [math]\displaystyle{ A2 }[/math] invariants:

The [math]\displaystyle{ A2 }[/math] invariant attains values on the knots and links known to KnotTheory:

[Khovanov] ^  M. Khovanov, [math]\displaystyle{ sl(3) }[/math] 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.