On Weyl modules over affine Lie algebras in prime characteristic

TL;DR

This paper constructs homomorphisms between Weyl modules over affine Lie algebras in characteristic p, supporting a conjecture on linkage principles and revealing reducible modules beyond level one.

Contribution

It introduces new homomorphisms between Weyl modules and provides evidence for the strong linkage principle in prime characteristic.

Findings

Constructed a family of homomorphisms supporting the linkage conjecture

Identified a large class of reducible Weyl modules beyond level one

Extended understanding of module reducibility in prime characteristic

Abstract

We construct a family of homomorphisms between Weyl modules for affine Lie algebras in characteristic p, which supports our conjecture on the strong linkage principle in this context. We also exhibit a large class of reducible Weyl modules beyond level one, for p not necessarily small.