Wakimoto realization of Drinfeld current for the elliptic quantum algebra $U_{q,p}(sl_3^)$

TL;DR

This paper develops a free field realization of the elliptic quantum algebra U_{q,p}(sl_3) for any level, generalizing Wakimoto's realization of affine Lie algebras and connecting to elliptic analogues of Drinfeld currents.

Contribution

It introduces a novel free field realization of the elliptic quantum algebra U_{q,p}(sl_3) for arbitrary level, extending Wakimoto's realization to elliptic cases.

Findings

Realization reproduces Wakimoto's for sl_3 in the limit p→0, q→1

Provides explicit construction of elliptic Drinfeld currents

Extends free field methods to elliptic quantum algebras

Abstract

We study a free field realization of the elliptic quantum algebra $U_{q,p}(sl_3^)$ for arbitrary level $k$. We give the free field realization of elliptic analogue of Drinfeld current associated with $U_{q,p}(sl_3^)$ for arbitrary level $k$. In the limit $p \to 0, q \to 1$ our realization reproduce Wakimoto realization for the affine Lie algebra $sl_3^$.