We study character generating functions (character generators) of simple Lie algebras. The
expression due to Patera and Sharp, derived from the Weyl character formula, is ¯rst re-
viewed. A new general formula is then found. It makes clear the distinct roles of \outside"
and \inside" elements of the integrity basis, and helps determine their quadratic incompati-
bilities. We review, analyze and extend the results obtained by Gaskell using the Demazure
character formulas. We ¯nd that the fundamental generalized-poset graphs underlying the
character generators can be deduced from such calculations. These graphs, introduced by
Baclawski and Towber, can be simpli¯ed for the purposes of constructing the character
generator. The generating functions can be written easily using the simpli¯ed versions,
and associated Demazure expressions. The rank-two algebras are treated in detail, but we
believe our results are indicative of those for general simple Lie algebras. / vii, 92 leaves ; 29 cm.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:ALU.w.uleth.ca/dspace#10133/532 |
| Date | January 2006 |
| Creators | Okeke, Nnamdi, University of Lethbridge. Faculty of Arts and Science |
| Contributors | Walton, Mark |
| Publisher | Lethbridge, Alta. : University of Lethbridge, Faculty of Arts and Science, 2006, Faculty of Arts and Science, Department of Physics |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
| Relation | Thesis (University of Lethbridge. Faculty of Arts and Science) |
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