2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/103882We take some initial steps towards illuminating the (hypothetical) $p$-adic local Langlands functoriality principle relating Galois representations of a $p$-adic field $L$ and admissible unitary Banach space representations of $G(L)$ when $G$ is a split reductive group over $L$. The outline of our work is derived from Breuil's remarkable insights into the nature of the correspondence between 2-dimensional crystalline Galois representations of the Galois group of $\Qdss_p$ and Banach space representations of $GL_{2}(\Qdss_p)$.Dedicated to John Coates on his 60th birthdayNumber TheoryRepresentation Theory11S37, 22E50text