Locally analytic vectors in representations of locally p-adic analytic groups / Matthew Emerton.

Format:

Book

Author/Creator:

Emerton, Matthew, author.

Series:

Memoirs of the American Mathematical Society ; Volume 248, number 1175.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 248, number 1175

Language:

English

Subjects (All):

p-adic analysis.

p-adic groups.

Representations of groups.

Geometry, Analytic.

Physical Description:

1 online resource (168 pages).

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2017.

Summary:

The goal of this memoir is to provide the foundations for the locally analytic representation theory that is required in three of the author's other papers on this topic. In the course of writing those papers the author found it useful to adopt a particular point of view on locally analytic representation theory: namely, regarding a locally analytic representation as being the inductive limit of its subspaces of analytic vectors (of various "radii of analyticity"). The author uses the analysis of these subspaces as one of the basic tools in his study of such representations. Thus in this memoir he presents a development of locally analytic representation theory built around this point of view. The author has made a deliberate effort to keep the exposition reasonably self-contained and hopes that this will be of some benefit to the reader.

Contents:

Cover

Title page

Introduction

0.1. Locally analytic vectors and locally analytic representations

0.2. The organization of the memoir

0.3. Terminology, notation, and conventions

Chapter 1. Non-archimedean functional analysis

1.1. Functional analytic preliminaries

1.2. Fréchet-Stein algebras

Chapter 2. Non-archimedean function theory

2.1. Continuous rigid analytic, and locally analytic functions

2.2. Distributions

2.3. Change of field

Chapter 3. Continuous, analytic, and locally analytic vectors

3.1. Regular representations

3.2. The orbit map and continuous vectors

3.3. Analytic vectors

3.4. Analytic vectors continued

3.5. Locally analytic vectors

3.6. Analytic and locally analytic representations

Chapter 4. Smooth, locally finite, and locally algebraic vectors

4.1. Smooth and locally finite vectors and representations

4.2. Locally algebraic vectors and representations

Chapter 5. Rings of distributions

5.1. Frobenius reciprocity and group rings of distributions

5.2. Completions of universal enveloping algebras

5.3. Rings of locally analytic distributions are Fréchet-Stein algebras

Chapter 6. Admissible locally analytic representations

6.1. Admissible locally analytic representations

6.2. Strongly admissible locally analytic representations and admissible continuous representations

6.3. Admissible smooth and admissible locally algebraic representations

6.4. Essentially admissible locally analytic representations

6.5. Invariant lattices

Chapter 7. Representations of certain product groups

7.1. Strictly smooth representations

7.2. Extensions of notions of admissibility for representations of certain product groups

Bibliography

Back Cover.

Notes:

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-4052-0