Acknowledgement
Supported by : Korea Research Foundation
Journal of the Chungcheong Mathematical Society (충청수학회지)
- Volume 5 Issue 1
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- Pages.195-201
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- 1992
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- 1226-3524(pISSN)
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- 2383-6245(eISSN)
Complete Reducibility of some Modules for a Generalized Kac Moody Lie Algebra
- Kim, Wansoon (Department of Mathematics Hoseo University)
- Received : 1992.06.30
- Published : 1992.07.31
Abstract
Let G(A) denote a generalized Kac Moody Lie algebra associated to a symmetrizable generalized Cartan matrix A. In this paper, we study on representations of G(A). Highest weight modules and the category O are described. In the main theorem we show that some G(A) modules from the category O are completely reducible. Also a criterion for irreducibility of highest weight modules is obtained. This was proved in [3] for the case of Kac Moody Lie algebras.
Keywords