Classification Of
نویسنده
چکیده
For any reductive Lie algebra g and commutative, associative, unital algebra S, we give a complete classification of the simple weight modules of g ⊗ S with finite weight multiplicities. In particular, any such module is parabolically induced from a simple admissible module for a Levi subalgebra. Conversely, all modules obtained in this way have finite weight multiplicities. These modules are isomorphic to tensor products of evaluation modules at distinct maximal ideals of S. Our results also classify simple Harish-Chandra modules up to isomorphism for all central extensions of current algebras.
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