Equivalences between three presentations of orthogonal and symplectic Yangians

We prove the equivalence of two presentations of the Yangian Y ( g ) of a simple Lie algebra g , and we also show the equivalence with a third presentation when g is either an orthogonal or a symplectic Lie algebra. As an application, we obtain an explicit correspondence between two versions of the classification theorem of finite-dimensional irreducible modules for orthogonal and symplectic Yangians.