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11 - Locally Analytic Representations of p-adic Groups

Published online by Cambridge University Press:  25 November 2023

Edited by
David Jordan ,
Nadia Mazza  and
Sibylle Schroll
David Jordan
Affiliation:
University of Edinburgh
Nadia Mazza
Affiliation:
Lancaster University
Sibylle Schroll
Affiliation:
Universität zu Köln
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Summary

This is a survey of Schneider and Teitelbaum’s theory of admissible locally analytic representations of p-adic Lie groups. We explain the basic definitions of p-adic Lie groups and their locally analytic representations. We then introduce the distribution algebra D(G,K) of a p-adic Lie group G and prove that it is a Fréchet–Stein algebra when G is compact. This allows us to define a nice abelian category of admissible representations for any p-adic Lie group G. We finish by briefly describing more recent developments in the theory.

Keywords

p-adic Lie groupslocally analytic representationsdistribution algebra
Type
Chapter
Information
Modern Trends in Algebra and Representation Theory , pp. 370 - 395
Publisher: Cambridge University Press
Print publication year: 2023

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