Naihuan Jing, Ming Liu, Alexander Molev, “Representations of Quantum Affine Algebras in their <nobr>$R$</nobr>-Matrix Realization”, SIGMA, 2020, Volume 16,145, 25 pp.

This article is cited in 1 paper

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

Naihuan Jing^a, Ming Liu^b, Alexander Molev^c

^a Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA
^b School of Mathematics, South China University of Technology, Guangzhou, 510640, China
^c School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia

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.

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

MSC: 17B37

Received: August 19, 2020; in final form December 25, 2020; Published online December 28, 2020

Language: English

DOI: 10.3842/SIGMA.2020.145