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

TL;DR

This paper conjectures bounds on prime characteristics ensuring irreducibility of modules for affine sl_2 and Virasoro algebra, and discusses the validity of the Goddard-Kent-Olive coset construction.

Contribution

It proposes explicit bounds on prime characteristics for module irreducibility and the applicability of the coset construction in affine sl_2 and Virasoro algebra.

Findings

Conjectured bounds on prime characteristic for irreducibility

Conditions for the validity of the Goddard-Kent-Olive coset construction

Implications for representation theory in modular settings

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.