2026/07/20 by Arpit Das, Sunil Mukhi
#hep-th #math-ph #math.MP #math.NT #math.QA #math.RT
Characters of rational conformal field theories solve modular linear differential equations labelled by their order and the Wronskian index ℓ. Direct classification of admissible solutions by solving MLDEs becomes increasingly difficult at higher ℓ -- where movable poles and accessory parameters appear. In this work we introduce differential operators that relate higher-ℓ solutions to lower-ℓ ones while preserving modular covariance and integrality of the \(q\)-series. In rank two, this generates all allowed Wronskian sectors from the Mathur--Mukhi--Sen equation. In rank three and higher, it reduces the construction of higher-ℓ quasi-characters to simpler equations with lower ℓ. This gives an efficient new route for organising candidate RCFT characters, and more generally quasi-characters, across the Wronskian tower. As an application, we apply our construction to prove a previously conjectured property on the signs of ℓ=2 quasi-characters in rank 2.