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.