New Jacobi-like identities for ZK parafermion characters

We state and prove various new identities involving the ZK parafermion characters (or level-K string functions) cn1 for the cases K=4, K=8, and K=16. These identities fall into three classes: identities in the first class are generalizations of the famous Jacobi θ-function identity (which is the K=2 special case), identities in another class relate the level K>2 characters to the Dedekind η-function, and identities in a third class relate the K>2 characters to the Jacobi θ-functions. These identities play a crucial role in the interpretation of fractional superstring spectra by indicating spacetime supersymmetry and aiding in the identification of the spacetime spin and statistics of fractional superstring states. (orig.)