**Edit**: As pointed out in the comment below, the question is about knot polynomials constructed out of the R-matrix, whence my original answer is not relevant.  I'll leave it here just in case someone else misunderstands the question.


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Of course you can.  In the [Chern-Simons approach of Witten's][1] you can get knot polynomials for any compact simple Lie group.  (In fact, Chern-Simons theory for noncompact Lie groups is still not well-understood despite continuing progress, reviewed in a [very recent paper of Witten's][2].)  In fact, the knot polynomial associated to $\mathfrak{so}(3)$ is the Jones polynomial.


  [1]: http://projecteuclid.org/euclid.cmp/1104178138
  [2]: http://arxiv.org/abs/1001.2933