Representations admitting two pairs of supplementary invariant spaces

Lionel Bérard Bergery (1) , Thomas Krantz (1)

1 IECN - Institut Élie Cartan de Nancy

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.

Domaines: Théorie des représentations [math.RT]

Lionel Bérard Bergery, Thomas Krantz. Representations admitting two pairs of supplementary invariant spaces. 2007. ⟨hal-00142655v2⟩