Tensor product of irreducible representations of Hecke algebras are discuss
ed. It is found that the tensor product of irreps of Hecke algebras generat
es representations of Birman-Wenzl algebra C-f(r, q) with r = q(3) or -q(-3
). A procedure fbr the evaluation of tensor product coefficients (TPC's) of
H-f(q) circle H-f(q) down arrow C-f(r,q) is established when the represent
ations of C-f (r, q) remain irreducible. An example of deriving TPC's of H-
f(q) circle H-f (q) down arrow C-f (r, q) is given. It is also found that i
ndecomposable representation of C-4(r, q) occurs in the tensor product [211
] circle [31].