Invariant theory and eigenspaces for unitary reflection groups

Gustav I. Lehrer; Jean Michel

doi:10.1016/S1631-073X(03)00192-4

Group Theory

Invariant theory and eigenspaces for unitary reflection groups
[Invariants et espaces propres des groupes de réflexion complexes]

Présenté par : Jacques Tits

Gustav I. Lehrer ¹ ; Jean Michel ^2,³

¹ School of Mathematics and Statistics, University of Sydney, N.S.W. 2006, Australia
² LAMFA, Université de Picardie-Jules Verne, 33, rue Saint-Leu, 80039 Amiens cedex, France
³ Institut de mathématiques, Université Paris VII, 175, rue du Chevaleret, 75013 Paris, France

Comptes Rendus. Mathématique, Volume 336 (2003) no. 10, pp. 795-800.

Abstract (VO)
Résumé

We prove some variations of formulas of Orlik and Solomon in the invariant theory of finite unitary reflection groups, and use them to give elementary and case-free proofs of some results of Lehrer and Springer, in particular that an integer is regular for a reflection group G if and only if it divides the same number of degrees and codegrees.

En utilisant des variantes d'une formule de Orlik et Solomon relative aux invariants d'un groupe de réflexions complexes G, nous redémontrons de façon élémentaire deux résultats de Lehrer and Springer, en particulier le fait qu'un entier est régulier pour G si et seulement si il divise le même nombre de degrés et de codegrés. Notre preuve évite l'analyse cas par cas.

Reçu le : 2003-03-18
Accepté le : 2003-04-09
Publié le : 2003-05-10

DOI : 10.1016/S1631-073X(03)00192-4

Affiliations des auteurs :

Gustav I. Lehrer ¹ ; Jean Michel ^{2, 3}

¹ School of Mathematics and Statistics, University of Sydney, N.S.W. 2006, Australia
² LAMFA, Université de Picardie-Jules Verne, 33, rue Saint-Leu, 80039 Amiens cedex, France
³ Institut de mathématiques, Université Paris VII, 175, rue du Chevaleret, 75013 Paris, France

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Gustav I. Lehrer; Jean Michel. Invariant theory and eigenspaces for unitary reflection groups. Comptes Rendus. Mathématique, Volume 336 (2003) no. 10, pp. 795-800. doi : 10.1016/S1631-073X(03)00192-4. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00192-4/

Bibliographie
Cité par

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