Principal subspaces of twisted modules for certain lattice vertex operator algebras

TL;DR

This paper advances the understanding of principal subspaces in twisted modules of lattice vertex operator algebras, providing new presentations and recursive formulas for their multigraded dimensions.

Contribution

It develops new presentations for principal subspaces of twisted modules for lattices with non-negative Gram matrices, extending previous work and deriving recursive dimension formulas.

Findings

Presented generators and relations for principal subspaces.

Constructed exact sequences leading to recursive dimension formulas.

Calculated multigraded dimensions explicitly.

Abstract

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 $L$ 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 $V_L$. 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.