Nonexistence of modular fusion algebras whose kernels are certain noncongruence subgroups

摘要

A well-known conjecture states that the kernel of representation associated to a modular fusion algebra is always a congruence subgroup. Assuming this conjecture, Eholzer studied modular fusion algebras such that the kernel of representation associated to each of them is a congruence subgroup using the fact that all irreducible representaions of SL(2,Z/p~λZ) are classified. He classified all strongly modular fusion algebras of dimension two, three, four and the nondegenerate ones with dimension ≤ 24.