Character generators and graphs for simple lie algebras
Nnamdi Okeke · Open ULeth Scholarship (OPUS) (University of Lethbridge) · 2006
To my Parents 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 first 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 find 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 simplified for the purposes of constructing the character generator. The generating functions can be written easily using the simplified 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. iv Acknowledgements I am very grateful to MarkWalton whose supervision, encouragement and guidance were invaluable to the completion of this thesis. I wish to acknowledge all the members of the Physics Department at the University of Lethbridge for their support. My thanks go