Change of weights for locally analytic representations of ${\mathrm{GL}}_2({\mathbb{Q}}_{\mathrm{p}})$

Abstract

Let $D_1\subset D_2$ be $(\phi ,\Gamma )$-modules of rank $2$ over the Robba ring, and $\pi (D_1)$, $\pi (D_2)$ be the associated locally analytic representations of ${\mathrm{GL}}_2({\mathbb{Q}}_{\mathrm{p}})$ via the $p$-adic local Langlands correspondence. We describe the relation between $\pi (D_1)$ and $\pi (D_2)$.

arXiv comment19 pages