A note on modular properties of non-principal and non-coprincipal admissible C⁽¹⁾₂-modules of integer level

2025/12/11 by Minoru Wakimoto, Wakimoto, Minoru
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2512.10556

openalex publication_date 2025/12/11 · openalex created_date 2025/12/13 · openalex updated_date 2026/07/28

Abstract

For the affine Lie algebra C₂⁽¹⁾ we study non-principal and non-coprincipal admissible modules of integer level and their quantum Hamiltonian reduction, and show that they have Γ₀(2)-modular invariance.

Citations

• Modular Invariance of Characters for Affine Lie Algebras at Subprincipal Admissible Levels
• On modular invariance of quantum affine W-algebras
• Vanishing of the quantum reduction of the Deligne exceptional series representations of negative integer level
• On characters of irreducible highest weight modules of negative integer level over affine Lie algebras
• Modularity of Relatively Rational Vertex Algebras and Fusion Rules of Principal Affine W-Algebras

Related

• Modular Invariance of Characters for Affine Lie Algebras at Subprincipal Admissible Levels
• On modular invariance of quantum affine W-algebras
• Integrable and Weyl modules for quantum affine sl₂
• Modularity of admissible-level \mathfraksl₃ minimal models with denominator 2
• Representations of superconformal algebras and mock theta functions