q-centralizer algebras for spin groups

Let V and Vε be the vector and a spinor representation of , . We show that the quantum group and the braid group corresponding to the Dynkin diagram Bf (the latter acting via R-matrices) are each others commutant on Vε V f. Moreover, these braid representations factor through specializations of Häring–Oldenburgʹs B-BMW-algebra; this also holds with Vε replaced by Vmε, , if N is even. We use this observation to compute the weights of the Markov trace of this algebra as a 2-variable function, and the values of the parameters for which it is semisimple.