Infinite product decomposition of orbifold mapping spaces

Abstract

Physicists showed that the generating function of orbifold elliptic genera of symmetric orbifolds can be written as an infinite product. We show that there exists a geometric factorization on space level behind this infinite product formula, and we do this in the much more general framework of orbifold mapping spaces, where factors in the infinite product correspond to finite connected coverings of domain spaces whose fundamental groups are not necessarily abelian. From this formula, a concept of geometric Hecke operators for functors emerges. This is a nonabelian geometric generalization of the usual Hecke operators. We show that these generalized Hecke operators indeed satisfy the identity of the usual Hecke operators for the case of $2$–dimensional tori.