Tensor products of Hecke algebras

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].