Character generators and graphs for simple lie algebras

Thumbnail Image
Okeke, Nnamdi
University of Lethbridge. Faculty of Arts and Science
Journal Title
Journal ISSN
Volume Title
Lethbridge, Alta. : University of Lethbridge, Faculty of Arts and Science, 2006
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.
Dissertations, Academic , Lie algebras -- Research , Lie groups -- Research