Physics – Mathematical Physics
Scientific paper
2007-02-06
J.Phys.A: Math.Theor. 40 (2007) 8873-8901
Physics
Mathematical Physics
50 pages, 11 figures
Scientific paper
10.1088/1751-8113/40/30/017
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 reviewed. 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 incompatibilities. 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.
Okeke N.
Walton Mark A.
No associations
LandOfFree
On character generators for simple Lie algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On character generators for simple Lie algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On character generators for simple Lie algebras will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-427445