  The affine and degenerate affine Birman-Murakami-Wenzl (BMW) algebras arise
naturally in the context of Schur-Weyl duality for orthogonal and symplectic
quantum groups and Lie algebras, respectively. Cyclotomic BMW algebras, affine
and cyclotomic Hecke algebras, and their degenerate versions are quotients. In
this paper we explain how the affine and degenerate affine BMW algebras are
tantalizers (tensor power centralizer algebras) by defining actions of the
affine braid group and the degenerate affine braid algebra on tensor space and
showing that, in important cases, these actions induce actions of the affine
and degenerate affine BMW algebras. We then exploit the connection to quantum
groups and Lie algebras to determine universal parameters for the affine and
degenerate affine BMW algebras. Finally, we show that the universal parameters
are central elements--the higher Casimir elements for orthogonal and symplectic
enveloping algebras and quantum groups.
