Locally Analytic Vectors in Representations of Locally

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.

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.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.