Un théorème de densité analytique pour les groupes semisimples. (An analytic density theorem for semisimple groups) (Q1118047)

Suppose G is a connected real semi-simple linear group whose simple factors are all non-compact. Consider a representation of G on a locally convex topological vector space V. The author proves that if \(v\in V\) is analytic and is fixed under the action of a cocompact subgroup of G, then v is also fixed by G. This is a good generalization of the classical result of \textit{A. Weil} [Ann. Math., II. Ser. 75, 578-602 (1962; Zbl 0131.266)] for V of finite dimension (in which case all vectors are analytic). A principal ingredient of the author's proof is a holomorphic extension theorem due to Lescure. For completeness, he provides an alternative proof of this theorem by reducing it to a classical Hartogs' argument for \({\mathfrak sl}(2)\).