On the structure and characters of weight modules
-
Dimitar Grantcharov
Abstract
Let 𝔤 be a classical Lie superalgebra of type I or a Cartan-type Lie superalgebra W(n). We study weight 𝔤-modules using a method inspired by Mathieu's classification of the simple weight modules with finite weight multiplicities over reductive Lie algebras, [Mathieu O.: Classification of irreducible weight modules. Ann. Inst. Fourier 50 (2000), 537–592]. Our approach is based on the fact that every simple weight 𝔤-module with finite weight multiplicities is obtained via a composition of a twist and localization from a highest weight module. This allows us to transfer many results for category 𝒪 modules to the category of weight modules with finite weight multiplicities. As a main application of the method we reduce the problems of finding a 𝔤0-composition series and a character formula for all simple weight modules to the same problems for simple highest weight modules. In this way, using results of Serganova we obtain a character formula for all simple weight W(n)-modules and all simple atypical nonsingular 
-modules. Some of our results are new already in the case of a classical reductive Lie algebra 𝔤.
© Walter de Gruyter
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- Cohomology of harmonic forms on Riemannian manifolds with boundary
- On the structure and characters of weight modules
- On the vanishing of Ext over formal triangular matrix rings
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Articles in the same Issue
- A summation formula for divisor functions associated to lattices
- On a relative Alexandrov-Fenchel inequality for convex bodies in Euclidean spaces
- Cohomology of harmonic forms on Riemannian manifolds with boundary
- On the structure and characters of weight modules
- On the vanishing of Ext over formal triangular matrix rings
- Homotopy localization of groupoids
- A group-theoretic characterization of the direct product of a ball and a Euclidean space
- Degree-regular triangulations of the double-torus
- Generalized E-algebras over valuation domains
