2004/03/21 by Jean-Louis Clerc, Clerc, Jean-Louis, Khalid Koufany +1
Mathematics · #15A66 #32M15 #53D12 #Differential Geometry (math.DG) #FOS: Mathematics #Group Theory (math.GR) #math.DG #math.GR #msc:15A66 #msc:32M15 #msc:53D12
paper · pdf · doi:10.48550/arxiv.math/0403330
39 pages; 2 figures; uses xy-pic; New Version Comment : A few typos corrected
arxiv created 2004/03/21 · arxiv updated 2009/12/01
Let D be a Hermitian symmetric space of tube type, and let S be its Shilov boundary. We give a realization of the universal covering \widetildeS of S. Then we describe on \widetildeS a primitive for the generalized Maslov cocycle as defined in [\it Transform. Groups \bf 6 (2001), 303-320] and [\it J. Math. Pures Appl. \bf 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.