Braids inside the Birman–Wenzl–Murakami algebra

Abstract

We determine the Zariski closure of the representations of the braid groups that factor through the Birman–Wenzl–Murakami algebra, for generic values of the parameters $\alpha ,s$. For $\alpha ,s$ of modulus 1 and close to 1, we prove that these representations are unitarizable, thus deducing the topological closure of the image when in addition $\alpha ,s$ are algebraically independent.