Isomorphism between the $R$-matrix and Drinfeld presentations of quantum affine algebra: types $B$ and $D$

Naihuan Jing, Ming Liu and Alexander Molev

Abstract

Following the approach of Ding and I. Frenkel (1993) for type $A$, we showed in our previous work that the Gauss decomposition of the generator matrix in the $R$-matrix presentation of the quantum affine algebra yields the Drinfeld generators in all classical types. Complete details for type $C$ were given therein, while the present paper deals with types $B$ and $D$. The arguments for all classical types are quite similar so we mostly concentrate on necessary additional details specific to the underlying orthogonal Lie algebras.