A note on modular properties of non-principal and non-coprincipal admissible $C^{(1)}_2$-modules of integer level

TL;DR

This paper investigates certain admissible modules of the affine Lie algebra $C_2^{(1)}$ at integer levels, demonstrating their $ ext{Gamma}_0(2)$-modular invariance through quantum Hamiltonian reduction.

Contribution

It introduces the modular properties of non-principal and non-coprincipal admissible modules of $C_2^{(1)}$ at integer levels, expanding understanding of their symmetry characteristics.

Findings

Admissible modules exhibit $ ext{Gamma}_0(2)$-modular invariance.

Quantum Hamiltonian reduction links modules to modular forms.

Results extend modular invariance to non-principal, non-coprincipal cases.

Abstract

For the affine Lie algebra $C_2^{(1)}$ we study non-principal and non-coprincipal admissible modules of integer level and their quantum Hamiltonian reduction, and show that they have $\Gamma_0(2)$-modular invariance.