On the structure and characters of weight modules
| dc.creator | Grantcharov, Dimitar | |
| dc.date | 2004-09-20 | |
| dc.date.accessioned | 2026-07-07T05:12:22Z | |
| dc.date.available | 2026-07-07T05:12:22Z | |
| dc.description | 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 $\mathfrak g$. | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/math/0409371 | |
| dc.identifier | http://arxiv.org/abs/math/0409371 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72554 | |
| dc.subject | Representation Theory | |
| dc.subject | 17B10 | |
| dc.title | On the structure and characters of weight modules | |
| dc.type | text |