Character generators and graphs for simple lie algebras
Loading...
Date
2006
Authors
Okeke, Nnamdi
University of Lethbridge. Faculty of Arts and Science
Journal Title
Journal ISSN
Volume Title
Publisher
Lethbridge, Alta. : University of Lethbridge, Faculty of Arts and Science, 2006
Abstract
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.
Description
vii, 92 leaves ; 29 cm.
Keywords
Dissertations, Academic , Lie algebras -- Research , Lie groups -- Research