Symmetries of abelian orbifolds

Abstract

Using the Polya Enumeration Theorem, we count with particular attention to C-3/Gamma up to C-6/Gamma, abelian orbifolds in various dimensions which are invariant under cycles of the permutation group S-D. This produces a collection of multiplicative sequences, one for each cycle in the Cycle Index of the permutation group. A multiplicative sequence is controlled by its values on prime numbers and their pure powers. Therefore, we pay particular attention to orbifolds of the form C-D/Gamma where the order of is p(alpha). We propose a generalization of these sequences for any D and any p.