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Representations of Quantum Affine Algebras in their $R$-Matrix Realization (2008.07847v2)
Published 18 Aug 2020 in math.RT and math.QA
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.