Representations of Quantum Affine Algebras in their $R$-Matrix Realization

Naihuan Jing ; Ming Liu ; Alexander Molev

Symmetry, integrability and geometry: methods and applications, Tome 16 (2020)

Résumé

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.

Détail

Keywords: $R$-matrix presentation, Drinfeld polynomials, highest weight representation
Mots-clés : Gauss decomposition.

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