Fusion rules of modular invariants
  Modular invariants satisfy remarkable fusion rules. Let $Z$ be a modular invariant associated to a braided subfactor $N\subset M$. The decomposition of the non-normalized modular invariants $Z Z^{*}$ and $Z^{*}Z$ into sums of normalized modular invariants is related to the decomposition of the full induced $M-M$ system of sectors. 
David E Evans