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We consider the sl(2)-module structure on the spaces of symbols of differential opera- tors acting on the spaces of weighted densities. We compute the necessary and sufficient integrability conditions of a given infinitesimal deformation of this structure and we prove that any formal deformation is equivalent to its infinitesimal part. We study also the super analogue of this problem getting the same results.
Comment: the revised version corrects some minor errors
Comment: Preprint from 2003
We study holonomy representations admitting a pair of supplementary faithful sub-representations. In particular the cases where the sub-representations are isomorphic respectively dual to each other are treated. In each case we have a closer look at the classification in small dimension.
We examine the lattice generated by two pairs of supplementary vector subspaces of a finite-dimensional vector space by intersection and sum, with the aim of applying the results to the study of representations admitting two pairs of supplementary invariant spaces, or one pair and a reflexive form. We show that such a representation is a direct sum of three canonical sub-representations which we characterize. We then focus on holonomy representations with the same property.
Comment: Latex file, 89 pages. Several misprints corrected. To appear in Advances in Mathematics
Comment: 29 pages, v2 : Leray-Serre spectral sequence replaced by Gysin sequence only, corrected typos
Comment: The french version (p. 1-9) is followed by a "moderately detailed" english summary (p. 9-15)
Comment: 43 pages, 5 figures, revised version
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