Fusion Rules For Affine Kac-Moody Algebras

Document Type

Book Chapter

Publication Date



Quantum Algebra, High Energy Physics - Theory, Representation Theory


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 Varadaragan tensor product theorem. Previous work of the author and collaborators on a different approach to fusion rules from elementary group theory is also exlained.


Part of the Contemporary Mathematics book series titled "Kac-Moody Lie Algebras and Related Topics"

Publisher Attribution

Final version published in Contemporary Mathematics, 343 (January 2003), published by the American Mathematical Society.