A generalization of intertwining operators for vertex operator algebras

TL;DR

This paper extends the concept of intertwining operators to N-graded weak modules over vertex operator algebras and explores their properties, including a formula relating their dimensions to Zhu algebra modules.

Contribution

It introduces a generalized framework for intertwining operators in the context of N-graded weak modules and derives a dimension formula under certain conditions.

Findings

Derived a formula for the dimensions of intertwining operators

Extended the notion of intertwining operators to N-graded weak modules

Analyzed properties of these generalized operators

Abstract

We generalize the notion of an intertwining operator to N-graded weak modules over a vertex operator algebra and study their properties. We show a formula for the dimensions of these intertwining operators in terms of modules over the Zhu algebras under some conditions on N-graded weak modules.