Browsing Mathematics by Author "Tuite, Michael P."
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The bosonic vertex operator algebra on a genus g Riemann surface
Tuite, Michael P.; Zuevsky, Alexander (201108)We discuss the partition function for the Heisenberg vertex operator algebra on a genus g Riemann surface formed by sewing handles to a Riemann sphere. In particular, it is shown how the partition can be computed by means ... 
Exceptional Vertex Operator Algebras and the Virasoro Algebra
Tuite, Michael P. (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
Mason, Geoffrey; Tuite, Michael P. (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 ... 
Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces II
Mason, Geoffrey; Tuite, Michael P. (2011)We continue our program to define and study $n$point correlation functions for a vertex operator algebra $V$ on a higher genus compact Riemann surface obtained by sewing surfaces of lower genus. Here we consider Riemann ... 
Generalised Moonshine and Abelian Orbifold Constructions
Tuite, Michael P. (1994)We consider the application of Abelian orbifold constructions in Meromorphic Conformal Field Theory (MCFT) towards an understanding of various aspects of Monstrous Moonshine and Generalised Moonshine. We review some of the ... 
A Generalized Vertex Operator Algebra for Heisenberg Intertwiners
Tuite, Michael P.; Zuevsky, Alexander (2011)We consider the extension of the Heisenberg vertex operator algebra by all its irreducible modules. We give an elementary construction for the intertwining vertex operators and show that they satisfy a complex parametrized ... 
Genus Two Meromorphic Conformal Field Theory
Tuite, Michael P. (1999)We construct the genus two (or two loop) partition function for meromorphic bosonic conformal field theories. We use a sewing procedure involving two genus one tori by exploiting an explicit relationship between the genus ... 
Genus Two Partition and Correlation Functions for Fermionic Vertex Operator Superalgebras I
Tuite, Michael P.; Zuevsky, Alexander (2010)We define the partition and $n$point correlation functions for a vertex operator superalgebra on a genus two Riemann surface formed by sewing two tori together. For the free fermion vertex operator superalgebra we obtain ... 
Genus two partition and correlation functions for fermionic vertex operator superalgebras II
Tuite, Michael P.; Zuevsky, Alexander (20181018)We define and compute the continuous orbifold partition function and a generating function for all npoint correlation functions for the rank two free fermion vertex operator superalgebra on a genus two Riemann surface ... 
The Genus Two Partition Function for Free Bosonic and Lattice Vertex Operator Algebras
Mason, Geoffrey; Tuite, Michael P. (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 ... 
Genus two virasoro correlation functions for vertex operator algebras
Tuite, Michael P.; Gilroy, Thomas (20161206)We consider all genus two correlation functions for the Virasoro vacuum descendants of a vertex operator algebra. These are described in terms of explicit generating functions that can be combinatorially expressed in terms ... 
Genus two zhu theory for vertex operator algebras
Tuite, Michael P.; Gilroy, Thomas (20161027)We consider correlation functions for a vertex operator algebra on a genus two Riemann surface formed by sewing two tori together. We describe a generalisation of genus one Zhu recursion where we express an arbitrary genus ... 
Monstrous and Generalized Moonshine and Permutation Orbifolds
Tuite, Michael P. (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 ... 
N=2 and N=4 subalgebras of super vertex operator algebras
Tuite, Michael P.; Mason, Geoffrey; Yamskulna, Gaywalee (IOP Publishing, 20180110)We develop criteria to decide if an N=2 or N=4 super conformal algebra is a subalgebra of a super vertex operator algebra in general, and of a super lattice theory in particular. We give some specific examples. 
On exceptional vertex operator (Super) algebras
Tuite, Michael P.; Van, Hoang Dinh (Springer, 20141001)We consider exceptional vertex operator algebras and vertex operator superalgebras with the property that particular Casimir vectors constructed from the primary vectors of lowest conformal weight are Virasoro descendents ... 
On Genus Two Riemann Surfaces Formed from Sewn Tori
Mason, Geoffrey; Tuite, Michael P. (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 ... 
On the Torus degeneration of the genus two partition function
Hurley, Donny; Tuite, Michael P. (World Scientific Publishing, 20130716)We consider the partition function of a general vertex operator algebra V on a genus two Riemann surface formed by sewing together two tori. We consider the nontrivial degeneration limit where one torus is pinched down ... 
Partition functions and chiral algebras.
Tuite, Michael P. (American Mathematical Society, 200705)We discuss recent work of the authors concerning correlation functions and partition functions for free bosons/fermions and the bc or ghost system. We compare and contrast the nature of the 1point functions at genus 1, ... 
Rational Generalised Moonshine from Abelian Orbifoldings of the Moonshine Module
Ivanov, Rossen I.; Tuite, Michael P. (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 $k$ ... 
Some Generalizations of the MacMahon Master Theorem
Tuite, Michael P. (2011)We consider a number of generalizations of the $\beta$extended MacMahon Master Theorem for a matrix. The generalizations are based on replacing permutations on multisets formed from matrix indices by partial permutations ...