Book contents
- Frontmatter
- Contents
- Contributors
- Preface
- Introduction
- 1 Auslander–Reiten Theory of Finite-Dimensional Algebras
- 2 τ-tilting Theory – an Introduction
- 3 From Frieze Patterns to Cluster Categories
- 4 Infinite-dimensional Representations of Algebras
- 5 The Springer Correspondence
- 6 An Introduction to Diagrammatic Soergel Bimodules
- 7 A Companion to Quantum Groups
- 8 Infinite-dimensional Lie Algebras and Their Multivariable Generalizations
- 9 An Introduction to Crowns in Finite Groups
- 10 An Introduction to Totally Disconnected Locally Compact Groups and Their Finiteness Conditions
- 11 Locally Analytic Representations of p-adic Groups
- References
11 - Locally Analytic Representations of p-adic Groups
Published online by Cambridge University Press: 25 November 2023
Book contents
- Frontmatter
- Contents
- Contributors
- Preface
- Introduction
- 1 Auslander–Reiten Theory of Finite-Dimensional Algebras
- 2 τ-tilting Theory – an Introduction
- 3 From Frieze Patterns to Cluster Categories
- 4 Infinite-dimensional Representations of Algebras
- 5 The Springer Correspondence
- 6 An Introduction to Diagrammatic Soergel Bimodules
- 7 A Companion to Quantum Groups
- 8 Infinite-dimensional Lie Algebras and Their Multivariable Generalizations
- 9 An Introduction to Crowns in Finite Groups
- 10 An Introduction to Totally Disconnected Locally Compact Groups and Their Finiteness Conditions
- 11 Locally Analytic Representations of p-adic Groups
- References
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.
- Type
- Chapter
- Information
- Modern Trends in Algebra and Representation Theory , pp. 370 - 395Publisher: Cambridge University PressPrint publication year: 2023
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