TOWARDS A CLASSIFICATION OF SU(2)CIRCLE-PLUS-CENTER-DOT-CENTER-DOT-CENTER-DOT-CIRCLE-PLUS-SU(2) MODULAR INVARIANT PARTITION-FUNCTIONS

The complete classification of Wess-Zumino-Novikov-Witten modular invariant partition functions is known for very few affine algebras and levels, the most significant being all levels of A1 and A2 and level 1 of all simple algebras. Here, the classification problem is addressed for the nicest high rank semisimple affine algebras: (A1(1)) ⊕r. Among other things, all automorphism invariants are found explicitly for all levels k=(kl...,kr), and the classification for A1(1)⊕A1(1) is completed for all levels k1, k2. The classification problem for (A1(1))⊕r is also solved for any levels ki with the property that for i ≠ j each gcd(ki+2,kj+2)≤3. In addition, some physical invariants are found which seem to be new. Together with some recent work by Stanev, the classification for all (A1(1))k ⊕r could now be within sight. © 1995 American Institute of Physics.