Wakimoto realization of the elliptic algebra $U_{q,p}(\hat{sl_N})$

TL;DR

This paper constructs a free field realization of the elliptic quantum algebra U_{q,p}(\hat{sl_N}) for arbitrary level, extending known realizations and analyzing associated currents, with a limit connecting to the q-Wakimoto realization.

Contribution

It provides a new free field realization of the elliptic algebra U_{q,p}(\hat{sl_N}) for arbitrary level, generalizing previous results and exploring associated currents.

Findings

Realization valid for arbitrary level k not equal to 0 or -N

Analysis of Drinfeld and screening currents for the algebra

Limit p → 0 recovers q-Wakimoto realization

Abstract

We construct a free field realization of the elliptic quantum algebra $U_{q,p}(\hat{sl_N})$ for arbitrary level $k \neq 0,-N$. We study Drinfeld current and the screening current associated with $U_{q,p}(\hat{sl_N})$ for arbitrary level $k$. In the limit $p \to 0$ this realization becomes $q$-Wakimoto realization for $U_q(\hat{sl_N})$.