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.

arXiv commentincludes a review of arXiv:1705.08155, arXiv:1903.00204 and arXiv:1911.03496

References in corpus (8)

• Braid Group Action and Quantum Affine Algebras
• Parabolic presentations of the Yangian Y(gl_n)
• On the R-matrix realization of Yangians and their representations
• Minimal Affinizations of Representations of Quantum Groups: the simply--laced case
• Off-shell Bethe vectors and Drinfeld currents
• Equivalences between three presentations of orthogonal and symplectic Yangians
• Isomorphism between the R-matrix and Drinfeld presentations of quantum affine algebra: type C
• Isomorphism between the $R$-Matrix and Drinfeld Presentations of Quantum Affine Algebra: Types $B$ and $D$

Cited by in corpus (2)

• Gaussian generators for the Yangian associated with the Lie superalgebra $\mathfrak{osp}(1|2m)$
• The R-matrix formalism for quantized enveloping algebras