Some conjectures on modular representations of affine $\mathfrak{sl}_2$ and Virasoro algebra

Abstract

We conjecture an explicit bound on the prime characteristic of a field, under which the Weyl modules of affine $\mathfrak{sl}_2$ and the minimal series modules of Virasoro algebra remain irreducible, and Goddard-Kent-Olive coset construction for affine $\mathfrak{sl}_2$ is valid.