On self-extensions of irreducible modules over symmetric groups, II

TL;DR

This paper investigates the conjecture that irreducible modules over symmetric groups do not admit non-trivial self-extensions in odd characteristic fields, providing improved partial results supporting this hypothesis.

Contribution

It advances the understanding of self-extensions of irreducible modules over symmetric groups by strengthening existing partial results.

Findings

Evidence supporting the conjecture that irreducible modules have no non-trivial self-extensions in odd characteristic

Improved partial results on the non-existence of self-extensions

Progress towards a full proof of the conjecture

Abstract

It is conjectured that irreducible representations of symmetric groups have no non-trivial self-extension over fields of odd characteristic. We improve on partial results showing evidence of this conjecture.