Lusztig induction and $\ell$-blocks of finite reductive groups

TL;DR

This paper introduces a unified way to classify $ ext{\ell}$-blocks of finite groups of Lie type using Lusztig's induction, focusing on $e$-Jordan-cuspidal pairs, enhancing understanding of their structure.

Contribution

It provides a new unified parametrization of $ ext{\ell}$-blocks in finite reductive groups using Lusztig's induction and $e$-Jordan-cuspidal pairs, advancing the theoretical framework.

Findings

Unified parametrization of $ ext{\ell}$-blocks achieved

Connection between Lusztig induction and block classification established

Framework applicable to quasi-simple finite groups of Lie type

Abstract

We present a unified parametrisation of $\ell$-blocks of quasi-simple finite groups of Lie type in non-defining characteristic via Lusztig's induction functor in terms of $e$-Jordan-cuspidal pairs and $e$-Jordan quasi-central cuspidal pairs.