Integral $Ext^2$ between hook Weyl modules

TL;DR

This paper computes the second extension groups between hook Weyl modules for the integral general linear group, providing detailed algebraic descriptions and implications for modular extensions.

Contribution

It introduces a detailed method to determine $Ext^2$ groups between hook Weyl modules, advancing understanding of their extension structures.

Findings

Explicit formulas for $Ext^2$ between hook Weyl modules

Determination of $Ext^1$ groups in modular settings

Enhanced understanding of extension relations in representation theory

Abstract

This paper concerns representations of the integral general linear group. The extension groups $Ext^2$ between any pair of hook Weyl modules are determined via a detailed study of cyclic generators and relations associated to certain extensions. As a corollary, the modular extension groups $Ext^1$ between such modules are determined.