Primitive du cocycle de Maslov généralisé

Jean-Louis Clerc (1) , Khalid Koufany (1)

1 IECN - Institut Élie Cartan de Nancy

Let $D$ be a Hermitian symmetric space of tube type, and let $S$ be its Shilov boundary. We give a realizaton of the universal covering $\tilde{S}$ of $S$. Then, we describe on $\tilde{S}$ a primitive for the generalized Maslov cocycle as defined in [Transform. Groups 6 (2001), 303-320] and [J. Math. Pures Appl. 83 (2004), 99-114]. It generalizes the Souriau index in the case of the Lagrangian manifold. A variation of this construction yields a generalization of the Arnold-Leray-Maslov index. This primitive is used to generalize the symplectic rotation number.

Domaines: Théorie des représentations [math.RT]

Jean-Louis Clerc, Khalid Koufany. Primitive du cocycle de Maslov généralisé. Mathematische Annalen, 2007, 337, pp.91-138. ⟨hal-00091301⟩