## 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.

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 Thursday, November 7, 2019