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Journal of the London Mathematical Society Advance Access originally published online on January 19, 2007
Journal of the London Mathematical Society 2007 75(1):187-198; doi:10.1112/jlms/jdl018
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© 2007 London Mathematical Society

On weakly eutactic forms

Anne-Marie Bergé and Jacques Martinet

A2X, Institut de Mathématiques
Université Bordeaux 1
351, cours de la Libération
33405 Talence cedex
France
berge{at}math.u-bordeaux.fr
martinet{at}math.u-bordeaux.fr

We make precise some properties of the Hermite function in relation with the Morse theory introduced by Avner Ash in his papers ‘On eutactic forms’,Canad. J. Math. 29 (1977) 1040–1054 and ‘On the existence of eutactic forms’,Bull. London Math. Soc. 12 (1980) 192–196, and with the cellular decomposition of the space of positive definite quadratic forms. We also establish a link between Ash's and Bavard's mass formulae.

2000 Mathematics Subject Classification 11H55.

Received December 9, 2005; published online January 19, 2007.


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