  We construct a [(n+1)/2]+1 parameters family of irreducible representations
of the Braid group B_3 in arbitrary dimension n\in N, using a q-deformation of
the Pascal triangle. This construction extends in particular results by
S.P.Humphries [8], who constructed representations of the braid group B_3 in
arbitrary dimension using the classical Pascal triangle. E.Ferrand [7] obtained
an equivalent representation of B_3 by considering two special operators in the
space C^n[X]. Slightly more general representations were given by I.Tuba and
H.Wenzl [11]. They involve [(n+1)/2] parameters (and also use the classical
Pascal 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 the equivalence of the representations.
  In [17] we establish the connection between the constructed representation of
the braid group B_3 and the highest weight modules of U(sl_2) and quantum group
U_q(sl_2).
