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

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

2009-02-07

arxiv.org/abs/0902.1273v2

Mathematics

Representation Theory

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Scientific paper

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.

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