On CRDAHA and finite general linear and unitary groups

TL;DR

This paper explores the relationship between Lusztig induction in finite groups and parabolic induction in affine Hecke algebras, providing new insights into modular representation theory and explaining existing bijection results.

Contribution

It establishes a novel connection between induction operators in finite groups and affine Hecke algebras, advancing understanding of modular representations.

Findings

Connected Lusztig induction with affine Hecke algebra induction

Explained Broué-Malle-Michel bijection

Derived results on modular decomposition numbers

Abstract

We show a connection between Lusztig induction operators in finite general linear and unitary groups and parabolic induction in cyclotomic rational double affine Hecke algebras. Two applications are given: an explanation of a bijection result of Brou\'e, Malle and Michel, and some results on modular decomposition numbers of finite general groups.