On the Faithfulness of Jones-Wenzl Representation of the Braid Group B4


We consider the Jones - Wenzl representation $\rho_{4}^{(k,r)}$ of the braid group $B_{4}$. For each pair of integers (k,r) with $r \geq k+1$, we exclude a family of words in the generators from belonging to the kernel of $\rho_{4}^{(k,r)}$. Then, we prove that $\rho_{4}^{(k,r)}$ is not faithful for any even integer r.

Journal/Conference Information

International Journal of Applied Mathematics,DOI:, ISSN: ISSN 1314-8060, Volume: 32, Issue: 3, Pages Range: 423-431,