Simplicities of VOAs Associated to Jordan Algebras of Type $B$ and Character Formulas for Simple Quotients

TL;DR

This paper explores the structure of certain vertex operator algebras linked to Jordan algebras of type B, constructing their simple quotients explicitly and deriving character formulas for specific cases, advancing understanding of their algebraic properties.

Contribution

It provides explicit constructions of simple quotients of VOAs associated with Jordan algebras of type B and computes their character formulas for particular parameter values.

Findings

Explicit simple quotient constructions for VOAs associated with Jordan algebras of type B.

Character formulas derived for simple quotients when r = -2n, n ≥ 1.

Enhanced understanding of the algebraic structure and representations of these VOAs.

Abstract

In ths paper we study the VOA $V_{\mathcal{J},r}$ constructed by Ashihara and Miyamoto, We construct simple quotients of $V_{\mathcal{J},r},r\in\mathbb{Z}_{\neq 0}$ explicitly using dual-pair type constructions. We also compute the character formula of the simple quotients when $r=-2n,n\geq 1$.