Fusion Rules for Affine Kac-Moody Algebras

Details Fusion Rules for Affine Kac-Moody Algebras Fusion Rules for Affine Kac-Moody Algebras

2002-12-31

arxiv.org/abs/math/0212387v2

Mathematics

Quantum Algebra

43 pp, LateX, 18 postscript figures. Paper for my talk at the Ramanujan International Symposium on Kac-Moody Lie Algebras and

Scientific paper

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.

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