Quelques propriétés des représentations sphériques pour les espaces symétriques réductifs

Let G H be a reductive symmetric space and suppose V is an admissible (g, K)-module of finite length possessing a linear functional T ε{lunate} Vsu which is fixed by h and H ∩ K. We prove that V can be mapped equivariantly into C^∞( G H) such that T becomes the pull-back of the Dirac measure at the origin. Essential in the proof is the fact that the formal power series of certain matrix coefficients of V satisfy a system of differential equations with regular singularities.