Representations admitting two pairs of supplementary invariant spaces

Details Representations admitting two pairs of supplementary invariant spaces Representations admitting two pairs of supplementary invariant spaces

2007-04-20

arxiv.org/abs/0704.2777v2

Mathematics

Representation Theory

Scientific paper

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.

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