Banach-Hecke algebras and p-adic Galois Representations

Abstract

We 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 birthday

References in corpus (1)

• Iwahori-Hecke Algebras

Cited by in corpus (10)

• The classification of irreducible admissible mod p representations of a p-adic GL_n
• A Satake isomorphism in characteristic p
• On the Breuil-Mézard conjecture
• The universal family of semi-stable p-adic Galois representations
• On the Breuil-Schneider conjecture: Generic case
• Eigenvarieties and invariant norms: Towards p-adic Langlands for U(n)
• A note on Integral Satake isomorphisms
• Existence de normes invariantes pour GL_2
• Locally unitary principal series representations of ${\mathrm{GL}}_{d+1}(F)$
• On the universal module of $p$-adic spherical Hecke algebras