REPRESENTATIONS LOCALEMENT ANALYTIQUES DE GL2 (Qp) ET θ, G)- MODULES

We extend the p-adic local Langlands correspondence for GL(2)(Q(p)) to a correspondence Delta -> Pi(Delta) between (theta, Gamma)-modules of rank 2 over the Robba ring and certain locally analytic representations of GL(2)(Q(p)). If. is isocline, one uses the existing correspondence; in the remaining cases one builds a GL(2)(Q(p))-module from parabolically induced locally analytic representations and their duals. This construction extends to GL(2)(F) if F is a finite extension of Qp, which suggests that the same should be true for the correspondence Delta -> Pi(Delta).