Representations of Quantum Affine Algebras in their 𝑅-Matrix Realization

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.