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It is well-known that the Gauss decomposition of the generator matrix in the$R$-matrix presentation of the Yangian in type $A$ yields generators of itsDrinfeld presentation. Defining relations between these generators are known inan explicit form thus providing an isomorphism between the presentations. Ithas been an open problem since the pioneering work of Drinfeld to extend thisresult to the remaining types. We give a solution for the classical types $B$,$C$ and $D$ by constructing an explicit isomorphism between the $R$-matrix andDrinfeld presentations of the Yangian. It is based on an embedding theoremwhich allows us to consider the Yangian of rank $n-1$ as a subalgebra of theYangian of rank $n$ of the same type.

Isomorphism between the $R$-matrix and Drinfeld presentations of Yangian in types $B$, $C$ and $D$