# On Imprimitive Representations of Finite Reductive Groups in Non-defining Characteristic

## TL;DR

This paper classifies Harish-Chandra imprimitive representations of finite reductive groups in non-defining characteristic, linking the problem to Iwahori-Hecke algebras and Morita equivalences, and extends results to classical groups.

## Contribution

It provides a classification of imprimitive representations in non-defining characteristic and connects them to algebraic structures like Iwahori-Hecke algebras and Morita equivalences.

## Key findings

- Classification of Harish-Chandra imprimitive representations.
- Reduction of the problem to quasi-isolated blocks.
- Extension of results to classical groups and Lusztig series.

## Abstract

In this paper, we begin with the classification of Harish-Chandra imprimitive representations in non-defining characteristic. We recall the connection of this problem to certain generalizations of Iwahori-Hecke algebras and show that Harish-Chandra induction is compatible with the Morita equivalence by Bonnaf\'{e} and Rouquier, thus reducing the classification problem to quasi-isolated blocks. Afterwards, we consider imprimitivity of unipotent representations of certain classical groups. In the case of general linear and unitary groups, our reduction methods then lead to results for arbitrary Lusztig series.