Symmetries of Abelian Orbifolds

Understand

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 Gamma is p^alpha.