Coherent families of weight modules of Lie superalgebras and an explicit description of the simple admissible sl(n+1| 1)-modules
✍ Scribed by Dimitar Grantcharov
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 270 KB
- Volume
- 265
- Category
- Article
- ISSN
- 0021-8693
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✦ Synopsis
Let g be a classical Lie superalgebra of type I. We introduce coherent families of weight g-modules with bounded weight multiplicities, and establish a correspondence between cuspidal and highest weight submodules of these families by extending Mathieu's work [Ann. Inst. Fourier 50 (2000) 537]. This enables us to reduce the description of the g 0 -module structure of arbitrary simple weight g-modules with bounded weight multiplicities to the g 0 -module structure of highest weight modules with bounded weight multiplicities. We then construct tensor coherent families for g = sl(n + 1| 1) which yield an explicit description of the g 0 -structure of an arbitrary simple weight module with bounded weight multiplicities. In particular, we show that for g = sl(n + 1| 1), the maximal length of an indecomposable g 0 -submodule of a simple weight module with bounded multiplicities equals 5.