Fusion Rules for Affine Kac-Moody Algebras
Abstract
This is an expository introduction to fusion rules for affine Kac-Moody algebras, with major focus on the algorithmic aspects of their computation and the relationship with tensor product decompositions. Many explicit examples are included with figures illustrating the rank 2 cases. New results relating fusion coefficients to tensor product coefficients are proved, and a conjecture is given which shows that the Frenkel-Zhu affine fusion rule theorem can be seen as a beautiful generalization of the Parasarathy-Ranga Rao-Varadarajan tensor product theorem. Previous work of the author and collaborators on a different approach to fusion rules from elementary group theory is also explained.
Keywords
Cite
@article{arxiv.math/0212387,
title = {Fusion Rules for Affine Kac-Moody Algebras},
author = {Alex J. Feingold},
journal= {arXiv preprint arXiv:math/0212387},
year = {2007}
}
Comments
43 pp, LateX, 18 postscript figures. Paper for my talk at the Ramanujan International Symposium on Kac-Moody Lie Algebras and Applications, ISKMAA-2002, Jan. 28-31, 2002, Chennai, India. Important references and comments added. Final version accepted for publication. Also available from ftp://ftp.math.binghamton.edu/pub/alex/Madras_Paper_Latex.ps.gz