Weight 2 blocks of general linear groups and modular Alvis-Curtis duality

TL;DR

This paper explicitly determines the structure of weight 2 blocks and Alvis-Curtis duality for finite general linear groups in non-defining characteristic, advancing understanding of modular representation theory.

Contribution

It provides a detailed description of weight 2 blocks and computes the modular Alvis-Curtis duality for these blocks, a novel explicit calculation in the field.

Findings

Structure of weight 2 blocks and [2:1]-pairs of q-Schur algebras elucidated

Explicit computation of modular Alvis-Curtis duality for weight 2 blocks

Enhanced understanding of modular representation theory of general linear groups

Abstract

We obtain the structure of weight 2 blocks and [2:1]-pairs of q-Schur algebras, and compute explicitly the modular Alvis-Curtis duality for weight 2 blocks of finite general linear groups in non-defining characteristic.