Schneider, P.; Teitelbaum, J.

Banach-Hecke algebras and $p$-adic Galois representations

Doc. Math. (Bielefeld) Extra Vol. John H. Coates' Sixtieth Birthday, 631-684 (2006)


In this paper, 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 $L$.

Mathematics Subject Classification

11F80, 11S37, 22E50


$p$-adic local Langlands correspondence, Satake isomorphism, Iwahori-Hecke algebra, Banach-Hecke algebra, filtered isocrystal, crystalline Galois representation