Continuous representation theory of p-adic Lie groups
@inproceedings{Schneider2006ContinuousRT, title={Continuous representation theory of p-adic Lie groups}, author={Peter Schneider}, year={2006} }
In this paper we give an overview over the basic features of the continuous representation
theory of p-adic Lie groups as it has emerged during the last five years. Themain motivation
for developing such a theory is a possible extension of the local Langlands program to p-adic
Galois representations. This is still very much in its infancy. But in the last section we will
describe a first approximation to an extended Langlands functoriality principle for crystalline
Galois representations.
27 Citations
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40 References
Locally analytic distributions and p-adic representation theory
- Mathematics
- 1999
Let L be a finite extension of Qp, and let K be a spherically complete non-archimedean extension field of L. In this paper we introduce a restricted category of continuous representations of locally…
Invariant distributions on $p$-adic analytic groups
- Mathematics
- 2007
Let p be a prime number, L a finite extension of the field Qp of p-adic numbers, K a spherically complete extension field of L and G the group of L-rational points of a split reductive group over L.…
Banach space representations and Iwasawa theory
- Mathematics
- 2000
We develop a duality theory between the continuous representations of a compactp-adic Lie groupG in Banach spaces over a givenp-adic fieldK and certain compact modules over the completed group…
Modular Representations of p-adic Groups and of Affine Hecke Algebras
- Mathematics
- 2002
Introduction The congruences between automorphic forms and their appli cations to number theory are a motivation to study the smooth representations of a reductive p-adic group G over an…
First steps towards p-adic Langlands functoriality
- Mathematics
- 2006
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Banach-Hecke algebras and p-adic Galois Representations
- Mathematics
- 2005
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Duality for admissible locally analytic representations
- Mathematics
- 2004
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Algebras of p-adic distributions and admissible representations
- Mathematics
- 2003
Let G be a compact, locally L-analytic group, where L is a finite extension of Qp. Let K be a discretely valued extension field of L. We study the algebra D(G,K) of K-valued locally analytic…