THE LOW-LEVEL MODULAR-INVARIANT PARTITION-FUNCTIONS OF RANK-2 ALGEBRAS

Using the self-dual lattice method, we make a systematic search for modular-invariant partition functions of the affine algebras g(1) of g = A2, A1 + A1, G2, and C2. Unlike previous computer searches, this method is necessarily complete. We succeed in finding all physical invariants for A2 at levels less-than-or-equal-to 32, for G2 at levels less-than-or-equal-to 31, for C2 at levels less-than-or-equal-to 26, and for Al + Al at levels kl = k2 less-than-or-equal-to 21. This work thus completes a recent A2 classification proof, where the levels k = 3,5,6,9,12,15,21 had been left out. We also compute the dimension of the (Weyl-folded) commutant for these algebras and levels.