Conway invariant Jacobi forms on the Leech lattice

Abstract

In this paper we study Jacobi forms associated with the Leech lattice $\Lambda$ which are invariant under the Conway group ${\mathrm{Co}}_0$. We determine and construct generators of modules of both weak and holomorphic Jacobi forms of integral weight and fixed index $t\le 3$. As applications, (1) we find the modular linear differential equations satisfied by the holomorphic generators; (2) we determine the decomposition of many products of orbits of Leech vectors; (3) we calculate the intersection between orbits and Leech vectors; (4) we derive some conjugate relations among orbits modulo $t\Lambda$.

Final version, to appear in Forum Math

References in corpus (2)

• Weyl invariant Jacobi forms: a new approach
• Weyl invariant $E_8$ Jacobi forms and $E$-strings