Braid-group approach to deriving universal R matrices

A new method for deriving universal (R) over cap matrices from braid-group representation is discussed. In this case, universal (R) over cap operators can be defined and expressed in terms of products of braid-group generator s. An advantage of this method is that matrix elements of (R) over cap are rank-independent, leaving multiplicity problem concerning coproducts of the corresponding quantum groups untouched.