  A connection is made between the Krammer representation and the
Birman-Murakami-Wenzl algebra. Inspired by a dimension argument, a basis is
found for a certain irrep of the algebra, and relations which generate the
matrices are found. Following a rescaling and change of parameters, the
matrices are found to be identical to those of the Krammer representation. The
two representations are thus the same, proving the irreducibility of one and
the faithfulness of the other.
