On R-matrix representations of Birman-Murakami-Wenzl algebras

We show that to every local representation of the Birman-Murakami-Wenzl algebra defined by a skew-invertible R-matrix $R\in Aut(V\otimes V)$ one can associate pairings $V\otimes V\to C$ and $V^{\ast }\otimes V^{\ast }\to C$, where V is the representation space. Further, we investigate conditions under which the corresponding quantum group is of SO or Sp type.