Abstract
We show that the fusion rule for a modular invariant E8-type conformal field theory, which is constructed from the one for the A1(1) Kac-Moody algebra by naive extension, is not associative. Then by imposing further restrictions to this naive fusion rule, we obtain 10 associative fusion rules for the left-right symmetric E8-type conformal field theory. We also discuss the factorization property of the fusion rule into left and right sectors.
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