Representations of Vertex Operator Algebras $V_{L_2}^{S_4}$ and $V_{L_2}^{A_5}$

TL;DR

This paper establishes the $C_2$ cofiniteness and rationality of certain vertex operator algebras, classifies their irreducible modules, and computes their quantum dimensions, advancing the understanding of their representation theory.

Contribution

It proves $C_2$ cofiniteness and rationality for $V_{L_2}^{S_4}$, classifies its irreducible modules, and determines modules for $V_{L_2}^{A_5}$ under these assumptions.

Findings

$V_{L_2}^{S_4}$ is $C_2$ cofinitive and rational.

All irreducible $V_{L_2}^{S_4}$-modules are classified.

Quantum dimensions of irreducible modules are calculated.

Abstract

$C_2$ cofiniteness and rationality of $V_{L_2}^{S_4}$ are obtained, and irreducible $V_{L_2}^{S_4}$-modules are classified. With the assumption of rationality and $C_2$ cofiniteness, irreducible $V_{L_2}^{A_5}$-modules are determined. Also, quantum dimensions of these irreducible modules are calculated.