Complétés universels de représentations de GL₂(Qₚ)

الأصل · EN

Let Pi be a unitary representation of GL₂(Qₚ), topologically of finite length. We describe the sub-representation Pian made of its locally analytic vectors, and its filtration by radius of analyticity, in terms of the phi-Gamma module attached to Pi via the p-adic local Langlands correspondence, and we deduce that the universal completion of Pian is Pi itself.