Symmetric cyclotomic Hecke algebras 

Gunter Malle and Andrew Mathas

Keywords

Cyclotomic Hecke algebras, complex reflection groups, symmetric algebras. 

Status

Submitted for publication.

Abstract

In this paper we prove that the generic cyclotomic Hecke algebras for 
imprimitive complex reflection groups are symmetric over any ring containing 
inverses of the parameters. For this we show that the determinant of the Gram 
matrix of a certain canonical symmetrizing form introduced in [BM] is a unit 
in any such ring. On the way we show that the Ariki-Koike bases of these 
algebras are also quasi-symmetric.