Métriques positives sur les espaces homogènes réductifs

Abstract

Let G be a real semi-simple Lie group and L be a reductive subgroup of G stable by the Cartan involution. We define a family of positive metrics on G / L parametrized by the points of G / K , where K is a maximal compact subgroup of G. We then use these metrics to generalize a lemma of Rawnsley, Schmid and Wolf from representation theory. We then show that the representation of G by left translation on the space of L 2 -forms on G / L is not uniformly bounded. To cite this article: N. Prudhon, C. R. Acad. Sci. Paris, Ser. I 345 (2007).