Representations of the vertex operator algebra V_{L_{2}}^{A_{4}}

TL;DR

This paper proves the rationality and C_2-cofiniteness of the orbifold vertex operator algebra V_{L_{2}}^{A_{4}} and classifies all its irreducible modules, contributing to the broader classification of rational VOAs with central charge 1.

Contribution

It establishes the rationality and C_2-cofiniteness of V_{L_{2}}^{A_{4}} and provides a complete classification of its irreducible modules, advancing the understanding of VOAs with c=1.

Findings

V_{L_{2}}^{A_{4}} is rational and C_2-cofinite

All irreducible modules of V_{L_{2}}^{A_{4}} are constructed and classified

Contributes to the classification of rational VOAs with c=1

Abstract

The rationality and C_2-cofiniteness of the orbifold vertex operator algebra V_{L_{2}}^{A_{4}} are established and all the irreducible modules are constructed and classified. This is part of classification of rational vertex operator algebras with c=1.