Modular invariants and isogenies

Classical Covariants and Modular Invariants

There is a relationship between the covariants of binary forms, a central topic in classical invariant theory, and the invariants of modular representations of cyclic groups of prime order. This relationship was identified by Gert Almkvist [1] and used implicitly in both [15] and [17]. In this note we investigate the relationship and provide a progress report on an application. Our primary moti...

Modular Forms and Projective Invariants

SU (3) Modular Invariants

Using N = 2 Landau-Ginzburg theories, we examine the recent conjectures relating the ̂ SU(3) WZW modular invariants, finite subgroups of SU(3) and Gorenstein singularities. All isolated three-dimensional Gorenstein singularities do not appear to be related to any known Landau-Ginzburg theories, but we present some curious observations which suggest that the SU(3)n/SU(2)×U(1) Kazama-Suzuki model ...

Spontaneous generation of modular invariants

It is possible to compute j(τ) and its modular equations with no perception of its related classical group structure except at ∞. We start by taking, for p prime, an unknown “p-Newtonian” polynomial equation g(u, v) = 0 with arbitrary coefficients (based only on Newton’s polygon requirements at ∞ for u = j(τ) and v = j(pτ)). We then ask which choice of coefficients of g(u, v) leads to some cons...

Subfactor realisation of modular invariants

We study the problem of realising modular invariants by braided subfactors and the related problem of classifying nimreps. We develop the fusion rule structure of these modular invariants. This structure is useful tool in the analysis of modular data from quantum double subfactors, particularly those of the double of cyclic groups, the symmetric group on 3 letters and the double of the subfacto...