A periodicity theorem for extensions of Weyl modules

TL;DR

This paper investigates periodicity patterns in modular extensions of Weyl and simple modules for the general linear group, focusing on how adding powers of the characteristic affects the structure of these modules.

Contribution

It introduces a periodicity theorem for extensions of Weyl modules, revealing new structural insights related to characteristic-based modifications of partitions.

Findings

Establishes a periodicity pattern in modular extensions

Connects module extensions to partition modifications involving powers of the characteristic

Provides a framework for understanding extension behaviors in modular representation theory

Abstract

In this paper we study periodicity phenomena for modular extensions between Weyl modules and between Weyl and simple modules of the general linear group that are associated to adding a power of the characteristic to the first parts of the involved partitions.