After a general review of Lie algebra theory, the generating function method describing the representations (or characters) of Lie algebras is introduced. The Demazure-Gaskell character formula for calculating a generating function is discussed in detail. / Using the concept of the depth of a weight i.e. the number of simple roots that are subtracted from the highest weight of a representation in order to arrive at a particular weight in that representation, the representations of affine Kac-Moody algebras are studied. The Demazure-Gaskell method is then applied to these representations, and the generating functions for the representations to finite depth are calculated. / Both complete representations and fully degenerate representations i.e. those whose highest weights contains only one non-zero weight component, are considered. Generating functions for complete and fully degenerate representations of affine Kac-Moody algebras are given.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.75988 |
| Date | January 1989 |
| Creators | Day, Lawrence Harvey |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Physics.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 000944904, proquestno: AAINL57186, Theses scanned by UMI/ProQuest. |
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