Abstract

We develop a systematic method to obtain the Feigin-Fuchs representations for arbitrary affine Lie algebras from a geometrical viewpoint. Choosing canonical coordinates for the flag manifolds associated with the Lie algebras, we get the general formulae for the KacMoody currents. In particular, we use this method to construct explicitly the Feigin-Fuchs representations for the affine Lie algebra of [Formula: see text] type.

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