On the definition of almost characters

TL;DR

This paper introduces a new explicit linear combination approach to define almost characters of finite reductive groups, extending previous definitions that required the center of the group to be connected.

Contribution

It generalizes the concept of almost characters to cases where the center of G may not be connected, providing a broader framework.

Findings

Defined almost characters as explicit linear combinations of irreducible characters.

Extended the definition of almost characters beyond the connected center case.

Provided a new framework for studying characters of finite reductive groups.

Abstract

We define the almost characters of G(F_q) where G is a reductive connected group over a finite field F_q as explicit linear combinations of irreducible characters. Previously these were defined assuming that the centre of G is connected.