Schur elements and basic sets for cyclotomic Hecke algebras

TL;DR

This paper investigates Schur elements and the a-function in cyclotomic Hecke algebras, establishing the existence of canonical basic sets for specific complex reflection groups, including finite Weyl groups with arbitrary parameters.

Contribution

It proves the existence of canonical basic sets for cyclotomic Hecke algebras associated with certain complex reflection groups, extending previous results to all parameters in characteristic zero.

Findings

Existence of canonical basic sets for certain complex reflection groups

Validation for finite Weyl groups with all parameter choices

Analysis of Schur elements and the a-function in this context

Abstract

We study the Schur elements and the a-function for cyclotomic Hecke algebras. As a consequence, we show the existence of canonical basic sets, as defined by Geck-Rouquier, for certain complex reflection groups. This includes the case of finite Weyl groups for all choices of parameters (in characteristic 0).