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We construct a [(n+1)/2]+1 parameters family of irreducible representationsof the Braid group B_3 in arbitrary dimension n\in N, using a q-deformation ofthe Pascal triangle. This construction extends in particular results byS.P.Humphries [8], who constructed representations of the braid group B_3 inarbitrary dimension using the classical Pascal triangle. E.Ferrand [7] obtainedan equivalent representation of B_3 by considering two special operators in thespace C^n[X]. Slightly more general representations were given by I.Tuba andH.Wenzl [11]. They involve [(n+1)/2] parameters (and also use the classicalPascal triangle). The latter authors also gave the complete classification ofall simple representations of B_3 for dimension n\leq 5. Our constructiongeneralize all mentioned results and throws a new light on some of them. Wealso study the irreducibility and the equivalence of the representations.  In [17] we establish the connection between the constructed representation ofthe braid group B_3 and the highest weight modules of U(sl_2) and quantum groupU_q(sl_2).

q-Pascal's triangle and irreducible representations of the braid group B_3 in arbitrary dimension