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The Finite Dimension Property of the Irreducible Representations of Noetherianp-Lie Algebras

โœ Scribed by M. A. Shevelin

Book ID
111611680
Publisher
SP MAIK Nauka/Interperiodica
Year
2004
Tongue
English
Weight
151 KB
Volume
45
Category
Article
ISSN
0037-4466

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๐Ÿ“œ SIMILAR VOLUMES

Computing dimensions of irreducible repr
Computing dimensions of irreducible representations of simple lie algebras
โœ A.K. Bose ๐Ÿ“‚ Article ๐Ÿ“… 1976 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 273 KB

We present a combinatorial algorithm for computing dimensions of irreducible representations of all nine types of simple Lie algebras over complexes. We implemented it on a programmable desk calculator. In conclusion some physical applications are discussed. ## Various formulas have been given [1-3

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We present an explicit description of the แ’…-support supp M of any irreducible แ’…-locally finite แ’„-module M, where แ’„ is any finite-dimensional Lie algebra and แ’… is an arbitrary nilpotent Lie subalgebra of แ’„. If แ’… contains a Cartan subalgebra of the semi-simple part of แ’„, we reformulate the description