Partial classification of modules for Lie-algebra of diffeomorphisms of d-dimensional torus

Abstract

We consider the Lie-algebra of the group of diffeomorphisms of d-dimensional torus which is also known to be the algebra of derivations on a Laurent polynomial ring A in d commuting variables denoted by DerA. Larsson has constructed a large class of DerA modules based on gl_d modules which are also A modules. In this paper we prove that any irreducible (A, DerA) module with finite dimensional weight spaces has to come from Larsson's construction.

The introduction has been rewritten and the connection to physics has been explained. Sevaral references related to physics has been added. Proof of Proposition (3.4) has been rewritten as there is a technical problem in the earlier version. Accepted in Journal of Mathematical Physics

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• Conformal fields: a class of representations of Vect(N)
• Lowest-energy representations of non-centrally extended diffeomorphism algebras
• Energy-momentum tensor for the toroidal Lie algebras
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