Free Field Realizations of the Elliptic Affine Lie Algebra sl(2,R)+\Omega_R/dR

TL;DR

This paper develops two free field realizations of the elliptic affine Lie algebra associated with sl(2,R), extending Wakimoto's construction and introducing new representations similar to Imaginary Verma modules.

Contribution

It presents the first Wakimoto-type realization and a novel class of representations for the elliptic affine Lie algebra sl(2,R) + _R/dR.

Findings

Constructed a Wakimoto-like realization for the elliptic affine Lie algebra.

Introduced new representations analogous to Imaginary Verma modules.

Extended free field realization techniques to elliptic affine Lie algebras.

Abstract

In this paper we construct two free field realizations of the elliptic affine Lie algebra sl(2,R) + \Omega_R/dR, where R=C[t,t^{-1},u|u^2=t^3 - 2b t^2 + t]. The first realization gives an analogue of Wakimoto's construction for Affine Kac-Moody algebras, but in the setting of the elliptic affine Lie algebra. The second realization gives new type of representations analogous to Imaginary Verma modules in the Affine setting.