ON THE CLASSIFICATION OF DIAGONAL COSET MODULAR INVARIANTS

We relate in a novel way the modular matrices of GKO diagonal cosets w ithout fixed points to those of WZNW tensor products. Using this we cl assify all modular invariant partition functions of su(3)(k) + su(3)(1 )/su(3)(k+1) for all positive integer level k, and su(2)(k) + su(2)(1) /su(2)(k+1) for all k and infinitely many l- (in fact, for each k a po sitive density of l). Of all these classifications, only that for su(2 )(k) + su(2)(1)/su(2)(k+1) had been known. Our lists include many new invariants.