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- W2951036884 abstract "Let $mathfrak g$ be a classical Lie superalgebra of type I or a Cartan-type Lie superalgebra {bf W}$(n)$. We study weight $mathfrak g$-modules using a method inspired by Mathieu's classification of the simple weight modules with finite weight multiplicities over reductive Lie algebras, cite{M}. Our approach is based on the fact that every simple weight $mathfrak g$-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 ${cal O}$ 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 ${mathfrak g}_0$-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 {bf W}$(n)$-modules and all simple atypical nonsingular ${mathfrak s}{mathfrak l} (m|1)$-modules. Some of our results are new already in the case of a classical reductive Lie algebra $mathfrak g$." @default.
- W2951036884 created "2019-06-27" @default.
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- W2951036884 date "2004-09-20" @default.
- W2951036884 modified "2023-10-12" @default.
- W2951036884 title "On the structure and characters of weight modules" @default.
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