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

TL;DR

This paper investigates how changing the underlying $(\

Contribution

It provides a detailed description of how the weights of locally analytic representations of $ m{GL}_2(\

Findings

Establishes a relation between representations associated to different $(\varphi, \Gamma)$-modules.

Clarifies the impact of weight changes on the structure of these representations.

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 $\pi(D_2)$.