Virasoro character identities from the Andrews--Bailey construction

TL;DR

This paper proves new q-series identities linking bosonic and fermionic forms of Virasoro characters, confirming some conjectures and using Bailey's lemma extensions.

Contribution

It introduces a novel application of Andrews' Bailey lemma extensions to establish Virasoro character identities, including conjectured cases.

Findings

Proved q-series identities between bosonic and fermionic Virasoro characters

Confirmed some conjectures from the Stony Brook group

Applied Bailey's lemma extensions to polynomial identities

Abstract

We prove $q$-series identities between bosonic and fermionic representations of certain Virasoro characters. These identities include some of the conjectures made by the Stony Brook group as special cases. Our method is a direct application of Andrews' extensions of Bailey's lemma to recently obtained polynomial identities.