Browsing Mathematics (Scholarly Articles) by Author "Tuite, Michael P."
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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 ... 
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 ... 
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 ... 
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 ... 
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 ... 
Some Irrational Generalised Moonshine from Orbifolds
Ivanov, Rossen I.; Tuite, Michael P. (2002)We verify the Generalised Moonshine conjectures for some irrational modular functions for the Monster centralisers related to the HaradaNorton, Held, $M_{12}$ and $L_3(3)$ simple groups based on certain orbifolding ... 
The Szegö Kernel on a Sewn Riemann Surface
Tuite, Michael P.; Zuevsky, Alexander (2010)We describe the Szegö kernel on a higher genus Riemann surface in terms of Szegö kernel data coming from lower genus surfaces via two explicit sewing procedures where either two Riemann surfaces are sewn together or a ... 
Torus Chiral nPoint Functions for Free Boson and Lattice Vertex Operator Algebras
Mason, Geoffrey; Tuite, Michael P. (2002)We obtain explicit expressions for all genus one chiral npoint functions for free bosonic and lattice vertex operator algebras. We also consider the elliptic properties of these functions. 
Torus nPoint Functions for $\mathbb{R}$graded Vertex Operator Superalgebras and Continuous Fermion Orbifolds
Mason, Geoffrey; Tuite, Michael P.; Zuevsky, Alexander (2007)We consider genus one npoint functions for a vertex operator superalgebra with a real grading. We compute all npoint functions for rank one and rank two fermion vertex operator superalgebras. In the rank two fermion case, ... 
Vertex Operators and Modular Forms
Mason, Geoffrey; Tuite, Michael P. (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 ... 
The Virasoro Algebra and Some Exceptional Lie and Finite Groups
Tuite, Michael P. (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 ... 
Virasoro Correlation Functions for Vertex Operator Algebras
Hurley, Donny; Tuite, Michael P. (2011)We consider all genus zero and genus one 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 ...