Mathieu Moonshine and symmetry surfing

Rademacher sums, Moonshine and Gravity

In 1939 Rademacher demonstrated how to express Klein’s modular invariant as a sum over elements of the modular group. In this article we generalize Rademacher’s approach so as to construct bases for the spaces of automorphic integrals of arbitrary even integer weight, for an arbitrary group commensurable with the modular group. Our methods provide explicit expressions for the Fourier expansions...

Rational Generalised Moonshine from Abelian Orbifoldings of the Moonshine Module

We consider orbifoldings of the Moonshine Module with respect to the abelian group generated by a pair of commuting Monster group elements with one of prime order p = 2, 3, 5, 7 and the other of order pk for k = 1 or k prime. We show that constraints arising from meromorphic orbifold conformal field theory allow us to demonstrate that each orbifold partition function with rational coefficients ...

Problems in moonshine

The talk at the I.C.C.M. was an introduction to moonshine. As there are already several survey articles on what is known about moonshine ([B94], [B99], [D-M94], [DM96], [F-H98], [J]), this paper differs from the talk and will concentrate mainly on what we do not know about it. Moonshine is not a well defined term, but everyone in the area recognizes it when they see it. Roughly speaking, it mea...

P. Mathieu

Monstrous and Generalized Moonshine and Permutation Orbifolds

We consider the application of permutation orbifold constructions towards a new possible understanding of the genus zero property in Monstrous and Generalized Moonshine. We describe a theory of twisted Hecke operators in this setting and conjecture on the form of Generalized Moonshine replication formulas.