Hecke algebras of normalizers of parabolic subgroups

TL;DR

This paper proves that under certain conditions, the generalized Hecke algebras of normalizers of parabolic subgroups in complex reflection groups are structured as semidirect products, advancing understanding of their algebraic properties.

Contribution

It establishes the semidirect product structure of these Hecke algebras, providing new insights into their algebraic composition in the context of complex reflection groups.

Findings

Hecke algebras of normalizers are semidirect products

Conditions on parameters ensure algebraic structure

Enhances understanding of algebraic properties of reflection groups

Abstract

In the context of Hecke algebras of complex reflection groups, we prove that the generalized Hecke algebras of normalizers of parabolic subgroups are semidirect products, under suitable conditions on the parameters involved in their definition.