## Representations of quantum affine algebras in their $$R$$-matrix realization

### Naihuan Jing, Ming Liu and Alexander Molev

#### Abstract

We use the isomorphisms between the $$R$$-matrix and Drinfeld presentations of the quantum affine algebras in types $$B$$, $$C$$ and $$D$$ produced in our previous work to describe finite-dimensional irreducible representations in the $$R$$-matrix realization. We also review the isomorphisms for the Yangians of these types and use Gauss decomposition to establish an equivalence of the descriptions of the representations in the $$R$$-matrix and Drinfeld presentations of the Yangians.

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 Thursday, August 20, 2020