## Search

Now showing items 1-10 of 11

#### Exceptional Vertex Operator Algebras and the Virasoro Algebra

(2008)

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 ...

#### Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces I

(2009)

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 ...

#### The Genus Two Partition Function for Free Bosonic and Lattice Vertex Operator Algebras

(2007)

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 ...

#### Vertex Operators and Modular Forms

(2009)

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 ...

#### Monstrous and Generalized Moonshine and Permutation Orbifolds

(2008)

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 ...

#### Rational Generalised Moonshine from Abelian Orbifoldings of the Moonshine Module

(2001)

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 $k$ ...

#### On Genus Two Riemann Surfaces Formed from Sewn Tori

(2006)

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 ...

#### Torus n-Point Functions for $\mathbb{R}$-graded Vertex Operator Superalgebras and Continuous Fermion Orbifolds

(2007)

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, ...

#### Some Irrational Generalised Moonshine from Orbifolds

(2002)

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 ...

#### The Virasoro Algebra and Some Exceptional Lie and Finite Groups

(2006)

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 ...