MODULAR INVARIANT PARTITION-FUNCTIONS AND METHOD OF SHIFT VECTOR

Using the shift vector method a large class of self-dual lattices of d imension (l,l) is obtained, which has a one to one correspondence with modular invariants of free bosonic theory compactified on a coroot la ttice of a rank l Lie group. Then a large number of modular invariants of affine Lie algebras are derived explicitly. Two applications of th is method are a direct derivation of the D series of SU(N) and a new p roof for the A-D-E classification of the SU(2)(k) partition functions.