Change of weights for locally analytic representations of $\rm{GL}_2(\mathbb{Q}_p)$

Abstract

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