Journal of Lie Theory 18 (2008), No. 1, 161--180
Copyright Heldermann Verlag 2008
L'Indice de Maslov en Dimension Infinie
Stéphane Merigon
Institut Elie Cartan, Université de Nancy, CNRS -- INRIA, Blv. Aiguillettes - B. P. 239, 54506 Vandoeuvre-les-Nancy, France
Stephane.Merigon@iecn.u-nancy.fr
Let E be a JB*-triple whose set of invertible tripotents Σ is not empty. We construct a homotopy invariant index for paths in Σ that satisfy a Fredholm type condition with respect to a fixed invertible tripotent. This index generalises the Maslov index for the Fredholm-Lagrangian of an infinite dimensional symplectic Hilbert space as defined by B. Booss-Bavnbek and K. Furutani ["The Maslov index: a functional analytical definition and the spectral flow formula", Tokyo Journal of Mathematics 21 (1998) 1--34]. When E is finite dimensional we make the connection with the generalised triple index of J.-L. Clerc and B. Oersted ["The Maslov index revisited", Transformation Groups 6 (2001) 303--320], and of J.-L. Clerc ["L'indice de Maslov généralisé, Journal de Mathématiques Pures et Appliquées, Neuvième Série 83 (2004) 99--114], and with the generalised Souriau index of J.-L. Clerc and K. Koufany ["Primitive du cocycle de Maslov généralisé, Mathematische Annalen 337 (2007) 91--138].
A correction to this article was published by the author in the Journal of Lie Theory 19 (2009), Number 1, 107--148.].
Keywords: Maslov index, bounded symmetric domains, Banach-Jordan algebras.
MSC: 53D12, 17C65, 32M15.
[ Fulltext-pdf (281 KB)] for subscribers only.