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In this paper we construct two free field realizations of the elliptic affineLie 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 AffineKac-Moody algebras, but in the setting of the elliptic affine Lie algebra. Thesecond realization gives new type of representations analogous to ImaginaryVerma modules in the Affine setting.

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