The center of the BMW algebras and an Okounkov-Vershik like approach

Abstract

We use the Jucys-Murphy elements of the BMW algebra to show that its center over the complex numbers for almost all parameters making it semisimple is given by Wheel Laurent polynomials, a subalgebra of the symmetric Laurent polynomials in the JM elements. As an application, we give an Okounkov-Vershik like approach to its finite dimensional representations. In the non semisimple case related to the type B Lie algebras, the central subalgebra of Wheel Laurent polynomials is large enough to separate blocks of the BMW algebras.