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 $k$ ...

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 ...

We obtain explicit expressions for all genus one chiral n-point functions for free bosonic and lattice vertex operator algebras. We also consider the elliptic properties of these functions.

We consider exceptional vertex operator algebras for which particular Casimir vectors constructed from the primary vectors of lowest conformal weight are Virasoro descendants of the vacuum. We discuss constraints on these ...

We define the partition and $n$-point functions for a vertex operator algebra on a genus two Riemann surface formed by sewing two tori together. We obtain closed formulas for the genus two partition function for the ...

We describe the period matrix and other data on a higher genus Riemann surface in terms of data coming from lower genus surfaces via an explicit sewing procedure. We consider in detail the construction of a genus two Riemann ...

We define the $n$-point function for a vertex operator algebra on a genus two Riemann surface in two separate sewing schemes where either two tori are sewn together or a handle is sewn to one torus. We explicitly obtain ...

We consider genus one n-point functions for a vertex operator superalgebra with a real grading. We compute all n-point functions for rank one and rank two fermion vertex operator superalgebras. In the rank two fermion case, ...

The leitmotif of these Notes is the idea of a vertex operator algebra (VOA) and the relationship between VOAs and elliptic functions and modular forms. This is to some extent analogous to the relationship between a finite ...

We describe a number of relationships between properties of the vacuum Verma module of a Virasoro algebra and the automorphism group of certain vertex operator algebras. These groups include the Deligne exceptional series ...