Espaces de représentations complètement réductibles

Anne Parreau (1)

1 IF - Institut Fourier

We study some geometric properties of actions on nonpositively curved spaces related to complete reducibility and semisimplicity, focusing on representations of a finitely generated group in the group G of rational points of a reductive group over a local field, acting on the associated space (symmetric space or affine building). We prove that the space of completely reducible classes is the maximal Hausdorff quotient space for the conjugacy action of G on the representation space.

Mots clés: nonpositive curvature; symmetric spaces; affine buildings; reductive groups over local fields; complete reducibility; moduli spaces of representations

Domaines: Théorie des groupes [math.GR]; Géométrie métrique [math.MG]; Théorie des représentations [math.RT]

Anne Parreau. Espaces de représentations complètement réductibles. Journal of the London Mathematical Society, 2011, 83, pp 545-562. ⟨hal-00396963v2⟩