(1) I see the paper gives the table of su(3) algebra and it says that it is the table of the su(3) algebra, I tend to agree that it is

.
(2) What I can not see in the paper is the concrete operations for each element of the table, or for a decent sample of them, so that any other student could reproduce it. No doubt you have done the operations in your head, but please draw them in the paper.
(3) Besides, my point is that if you have what you say, then a divide publish and conquer is in order. A paper "representation of the algebra su(3) in knot theory" deserves independent publication if you can do it.
(4) My impression by reading the whole paper is that you got the idea of su(2) relationship to feynmann candle dance trick and then you conjectured u(1) and su(3).