Abstract
We study induced modules of nonzero central charge with arbitrary multiplicities over affine Lie algebras. For a given pseudo parabolic subalgebra P of an affine Lie algeb- ra G, our main result establishes the equivalence between a certain category of P-induced G-modules and the category of weight P-modules with injective action of the central element of G. In particular, the induction functor preserves irreducible modules. If P is a parabolic subalgebra with a finite-dimensional Levi factor then it defines a unique pseudo parabolic subalgebra P ps , P P ps . The structure of P-induced modules in this case is fully deter- mined by the structure of P ps -induced modules. These results generalize similar reductions in particular cases previously considered by V. Futorny, S. Konig, V. Mazorchuk (Forum Math. 13 (2001), 641-661), B. Cox (Pacific J. Math. 165 (1994), 269-294) and I. Dimitrov, V. Futorny, I. Penkov (Comm. Math. Phys. 250 (2004), 47-63).
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