  In [1] we have constructed a [n+1/2]+1 parameters family of irreducible
representations of the Braid group B_3 in arbitrary dimension using a
$q-$deformation of the Pascal triangle. This construction extends in particular
results by S.P. Humphries (2000), who constructed representations of the braid
group B_3 in arbitrary dimension using the classical Pascal triangle. E.
Ferrand (2000) obtained an equivalent representation of B_3 by considering two
special operators in the space ${\mathbb C}^n[X].$ Slightly more general
representations were given by I. Tuba and H. Wenzl (2001). They involve [n+1/2]
parameters (and also use the classical Pascal's triangle). The latter authors
also gave the complete classification of all simple representations of $B_3$
for dimension $n\leq 5$. Our construction generalize all mentioned results and
throws a new light on some of them. We also study the irreducibility and
equivalence of the constructed representations.
  In the present article we show that all representations constructed in [1]
may be obtained by taking exponent of the highest weight modules of U(sl}_2 and
U_q(sl_2). We generalize these connections between the representation of the
braid group $B_n$ and the highest weight modules of the U_q(sl_{n-1}) for
arbitrary} n using the well-known reduced Burau representation.
