Irreducible representations for Toroidal Lie algebras

Details Irreducible representations for Toroidal Lie algebras Irreducible representations for Toroidal Lie algebras

2002-12-10

arxiv.org/abs/math/0212137v1

Mathematics

Representation Theory

19 pages

Scientific paper

We study irreducible modules for Toroidal Lie-algebras with finite dimensional weight spaces. First note that Toroidal Lie-algebras have infinite dimensional center. In genaral the infinite dimensional center does not act as scalars on an irreducible module but acts as invertible central operators. We prove in this paper the study of irreducible modules for Toroidal Lie-algebras with finite dimensional weight spaces is reduced to the study of irreducible modules where the center acts as scalars.

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