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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 ...
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, ...
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 ...
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 ...