The central elements of $E_{q,p}(\hat{sl_2})_k$ with the critical level

TL;DR

This paper extends results from quantum affine algebra at the critical level to elliptic quantum algebra $E_{q,p}(\uplushat{sl_2})$, constructing its central elements and confirming the Drinfeld conjecture in this elliptic context.

Contribution

It generalizes the construction of central elements and verifies the Drinfeld conjecture for elliptic quantum algebras at the critical level.

Findings

Central elements constructed at the critical level

Drinfeld conjecture confirmed for elliptic quantum algebras

Extension of Wakimoto realization to elliptic case

Abstract

In this paper we generalize certain results concerning quantum affine algebra $U_{q}(\hat{sl_{2}})$ at the critical level to the corresponding elliptic case $E_{q,p}(\hat{sl_2})$. Using the Wakimoto realization of the algebra $E_{q,p}(\hat{sl_2})$, we construct the central elements of it at the critical level. It turns out that the so called Drinfeld conjecture originally proposed for Kac-Moody algebras also holds for the elliptic quantum algebras.