  We determine the Zariski closure of the representations of the braid groups
that factorize 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.
