Fusion Rules For Affine Kac-Moody Algebras
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.
Final version published in Contemporary Mathematics, 343 (January 2003), published by the American Mathematical Society.
Feingold, A. J. (2004). Fusion rules for affine Kac-Moody algebras. Contemporary Mathematics, 343, 53-96. doi: 10.1090/conm/343/06184