Intertwining operators among modules for affine Lie algebra and lattice vertex operator algebras which respect integral forms

TL;DR

This paper introduces integral intertwining operators for modules of vertex operator algebras, classifies those respecting natural integral forms, and applies the classification to affine Lie algebra and lattice VOAs.

Contribution

It defines and characterizes integral intertwining operators and classifies them for specific classes of vertex operator algebras.

Findings

Integral intertwining operators are characterized by their action on generators.

Classification of integral intertwining operators for affine Lie algebra modules.

Classification of integral intertwining operators for lattice vertex operator algebra modules.

Abstract

We define an integral intertwining operator among modules for a vertex operator algebra to be an intertwining operator which respects integral forms in the modules, and we show that an intertwining operator is integral if it is integral when restricted to generators of the integral forms in the modules. We apply this result to classify integral intertwining operators which respect certain natural integral forms in modules for affine Lie algebra and lattice vertex operator algebras.