Conway invariant Jacobi forms on the Leech lattice

Abstract

In this paper, we study Jacobi forms associated with the Leech lattice A which are invariant under the Conway group Co-0. We determine and construct generators of modules of both weak and holomorphic Jacobi forms of integral weight and fixed index t <= 3. As applications, (1) we find the modular linear differential equations satisfied by the holomorphic generators; (ii) we determine the decompositions of many products of orbits of Leech vectors; (iii) we calculate the intersections between orbits and Leech vectors; (iv) we derive some conjugate relations among orbits modulo tA.