Darlayne Addabbo

activity

20162026

most citedOn generators and relations for higher level Zhu algebras and applications

6 citations · 6 across the 4 of their papers we have counts for

collaborators

7 papers

math.QA2026

The Huang Algebra Ideal and the Diagonal Shift Property

Darlayne Addabbo

Let $V$ be a grading-restricted vertex algebra and let $A^{\infty} (V) = U^{\infty} (V) / Q^{\infty} (V)$ be the associative algebra constructed by Huang, where $U^{\infty} (V)$ is the space of co…

math.QA2024

Modularity of Vertex Operator Algebra Correlators with Zero Modes

Darlayne Addabbo, Christoph A. Keller

It is known from Zhu's results that under modular transformations, correlators of rational $C_{2}$ -cofinite vertex operator algebras transform like Jacobi forms. We investigate the m…

math.RT2022

Vertex operators for imaginary $gl_{2}$ subalgebras in the Monster Lie Algebra

Darlayne Addabbo, Lisa Carbone, Elizabeth Jurisich +2

The Monster Lie algebra $m$ is a quotient of the physical space of the vertex algebra $V = V^{♮} \otimes V_{1, 1}$ , where $V^{♮}$ is the Moonshine module vertex ope…

math.QA2021★ 6 cited

On generators and relations for higher level Zhu algebras and applications

Darlayne Addabbo, Katrina Barron

We give some general results about the generators and relations for the higher level Zhu algebras for a vertex operator algebra. In particular, for any element $u$ in a vertex oper…

math.RT2016

Difference Hierarchies for $n T$ $τ$ -Functions

Darlayne Addabbo, Maarten Bergvelt

We introduce hierarchies of difference equations (referred to as $n T$ -systems) associated to the action of a (centrally extended, completed) infinite matrix group $GL_{\infty}^{(n)…

math.RT2016

$τ$ -Functions, Birkhoff Factorizations and Difference Equations

Darlayne Addabbo, Maarten Bergvelt

$Q$ -systems and $T$ -systems are systems of integrable difference equations that have recently attracted much attention, and have wide applications in representation theory and stat…