  We use some Lie group theory and Budney's unitarization of the
Lawrence-Krammer representation, to prove that for generic parameters of
definite form the image of the representation (also on certain types of
subgroups) is dense in the unitary group. This implies that, except possibly
for closures of full-twist braids, all links have infinitely many conjugacy
classes of braid representations on any non-minimal number of (and at least 4)
strands.
