Integrable representations of affine A(m,n) and C(m) superalgebras

We classify the irreducible zero-level integrable modules with finite dimensional weight spaces for the untwisted affine superalgebras Aˆ(m,n) (m≠n) and Cˆ(m). Such modules must be of highest weight type, but are not necessarily loop modules. This is in sharp contrast to the case of ordinary affine algebras. Combined with previous results obtained by other people (Rao and Zhao in particular), our work completes the program of classifying the irreducible integrable modules with finite dimensional weight spaces for all the untwisted affine superalgebras.