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Symmetric Cyclotomic Hecke Algebras

✍ Scribed by Gunter Malle; Andrew Mathas

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 236 KB
Volume: 205
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1997.7339

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✦ Synopsis

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 by K. Bremke and G. Malle Ž Ž . . Indag. Math. 8 1997 , 453᎐469 is a unit in any such ring. On the way we show that the Ariki᎐Koike bases of these algebras are also quasi-symmetric.

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