Symmetrizers and antisymmetrizers for the BMW-algebra

Let n ∈ N and B_n(r, q) be the generic Birman-Murakami-Wenzl algebra with respect to indeterminants r and q. It is known that B _n(r, q) has two distinct linear representations generated by two central elements of B_n(r, q) called the symmetrizer and antisymmetrizer of B_n(r, q). These generate for n ≥ 3 the only one-dimensional two sided ideals of B_n(r, q) and generalize the corresponding notion for Hecke algebras of type A. The main result, Theorem 3.1, in this paper explicitly determines the coefficients of these elements with respect to the graphical basis of B_n(r, q).