SYMMETRICAL CYCLOTOMIC HECKE ALGEBRAS

In this paper we prove that the generic cyclotomic Hecke algebras for imprimitive complex reflection groups are symmetric over any ring cont aining inverses of the parameters. For this we show that the determina nt of the Gram matrix of a certain canonical symmetrizing form introdu ced by K. Bremke and G. Malle (Indag. Math. 8 (1997), 453-469) is a un it in any such ring. On the way we show that the Ariki-Koike bases of these algebras are also quasi-symmetric. (C) 1998 Academic Press.