Some Irrational Generalised Moonshine from Orbifolds

Abstract

We verify the Generalised Moonshine conjectures for some irrational modular functions for the Monster centralisers related to the Harada-Norton, Held, $M_{12}$ and $L_3(3)$ simple groups based on certain orbifolding constraints. We find explicitly the fixing groups of the hauptmoduls arising in each case.