Three realizations of quantum affine algebra $U_q(A_2^{(2)})$

TL;DR

This paper establishes explicit isomorphisms between three different realizations of the quantum affine algebra $U_q(A_2^{(2)})$, providing a comprehensive understanding of its structure.

Contribution

It introduces explicit isomorphisms connecting the Drinfeld, Chevalley, and $RLL$ realizations of $U_q(A_2^{(2)})$, clarifying their relationships.

Findings

Explicit isomorphisms between three realizations

Unified framework for understanding $U_q(A_2^{(2)})$

Enhanced tools for quantum algebra research

Abstract

In this article we establish explicit isomorphisms between three realizations of quantum twisted affine algebra $U_q(A_2^{(2)})$: the Drinfeld ("current") realization, the Chevalley realization and the so-called $RLL$ realization, investigated by Faddeev, Reshetikhin and Takhtajan.