AUTOMORPHIC-FORMS AND LORENTZIAN KAC-MOODY ALGEBRAS - PART II

We give variants of lifting construction, which define new classes of modular forms on the Siegel upper half-space of complex dimension 3 wi th respect to the full paramodular groups (defining moduli of Abelian surfaces with arbitrary polarization). The data for these liftings are Jacobi forms of integral and half-integral indices. In particular, we get modular forms which are generalizations of the Dedekind eta-funct ion. Some of these forms define automorphic corrections of Lorentzian Kac-Moody algebras with hyperbolic generalized Cartan matrices of rank three classified in Part I of this paper. We also construct many auto morphic forms which give discriminants of moduli of K3 surfaces with c onditions on Picard lattice.