scholarly journals On Regularised Quantum Dimensions of the Singlet Vertex Operator Algebra and False Theta Functions

2016 ◽  
pp. rnw037 ◽  
Author(s):  
Thomas Creutzig ◽  
Antun Milas ◽  
Simon Wood
Keyword(s):  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Theta Functions ◽  
False Theta Functions ◽  
Quantum Dimensions

On characters of L𝔰𝔩n(−Λ0)-modules

2019 ◽  
Vol 22 (05) ◽  
pp. 1950030 ◽  
Author(s):  
Kathrin Bringmann ◽  
Karl Mahlburg ◽  
Antun Milas
Keyword(s):  
Asymptotic Expansion ◽  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Theta Functions ◽  
Asymptotic Behaviors ◽  
Highest Weight ◽  
False Theta Functions ◽  
Decomposition Formula ◽  
Quantum Dimensions

We use recent results of Rolen, Zwegers, and the first author to study the characters of irreducible (highest weight) modules for the vertex operator algebra [Formula: see text]. We establish asymptotic behaviors of characters for the (ordinary) irreducible [Formula: see text]-modules. As a consequence, we prove that their quantum dimensions are one, as predicted by the representation theory. We also establish a full asymptotic expansion of irreducible characters for [Formula: see text]. Finally, we determine a decomposition formula for the full characters in terms of unary theta and false theta functions which allows us to study their modular properties.

scholarly journals Uniqueness results for the moonshine vertex operator algebra

2007 ◽  
Vol 129 (2) ◽  
pp. 583-609 ◽  
Author(s):  
Chongying Dong ◽  
Robert L. Griess ◽  
Ching Hung. Lam
Keyword(s):  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Uniqueness Results ◽  
Moonshine Vertex Operator Algebra

scholarly journals VIRASORO CORRELATION FUNCTIONS FOR VERTEX OPERATOR ALGEBRAS

2012 ◽  
Vol 23 (10) ◽  
pp. 1250106 ◽  
Author(s):  
DONNY HURLEY ◽  
MICHAEL P. TUITE
Keyword(s):  
Graph Theory ◽  
Vertex Operator ◽  
Generating Functions ◽  
Operator Algebra ◽  
Correlation Functions ◽  
Vertex Operator Algebra ◽  
Operator Algebras ◽  
Vertex Operator Algebras ◽  
Genus Zero ◽  
Genus One

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 expressed in terms of graph theory related to derangements in the genus zero case and to partial permutations in the genus one case.

The radical of a vertex operator algebra

1998 ◽  
Author(s):  
C. Dong ◽  
H. Li, ◽  
G. Mason ◽  
P. S. Montague
Keyword(s):  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra

scholarly journals Principal subspaces of twisted modules for certain lattice vertex operator algebras

2019 ◽  
Vol 30 (10) ◽  
pp. 1950048 ◽  
Author(s):  
Michael Penn ◽  
Christopher Sadowski ◽  
Gautam Webb
Keyword(s):  
Algebraic Structure ◽  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Operator Algebras ◽  
Gram Matrix ◽  
Vertex Operator Algebras ◽  
Generators And Relations ◽  
The Third ◽  
Exact Sequences

This is the third in a series of papers studying the vertex-algebraic structure of principal subspaces of twisted modules for lattice vertex operator algebras. We focus primarily on lattices [Formula: see text] whose Gram matrix contains only non-negative entries. We develop further ideas originally presented by Calinescu, Lepowsky, and Milas to find presentations (generators and relations) of the principal subspace of a certain natural twisted module for the vertex operator algebra [Formula: see text]. We then use these presentations to construct exact sequences involving this principal subspace, which give a set of recursions satisfied by the multigraded dimension of the principal subspace and allow us to find the multigraded dimension of the principal subspace.

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