Modules for Yokonuma-type Hecke algebras

TL;DR

This paper studies module categories for a class of Hecke algebras related to complex reflection groups and finite general linear groups, constructing irreducible modules for their semisimple cases.

Contribution

It provides a detailed description of the module categories and explicitly constructs all irreducible modules for semisimple specializations of these algebras.

Findings

Complete sets of irreducible modules are constructed.

The module categories are characterized for the algebra family.

Connections to complex reflection groups and finite general linear groups are established.

Abstract

This paper describes the module categories for a family of generic Hecke algebras that specialize to the complex reflection groups G(r,1,n) and to the certain endomorphism rings of permutation characters of finite general linear groups. In particular, complete sets of inequivalent, irreducible modules for semisimple specializations of these algebras are constructed.