RESTRICTION OF $p$-MODULAR REPRESENTATIONS OF $p$-ADIC GROUPS TO MINIMAL PARABOLIC SUBGROUPS (Analytic, geometric and $p$-adic aspects of automorphic forms and $L$-functions)

This manuscript reports on an ongoing joint work with Julien Hauseux, on which is based the talk I gave on January 2020 at the RIMS workshop "Analytic, geometric and p-adic aspects of automorphic forms and £-functions". I thank Shunsuke Yamana for inviting me to participate to this very nice workshop and for the invitation to speak there. For more details on the work described below, e.g. statements in their full generality or further details of proofs, please refer to our paper with Hauseux [3]