Locally Analytic Vectors in Representations of Locally P-adic Analytic Groups
Locally Analytic Vectors in Representations of Locally P-adic Analytic Groups

Author: Matthew Emerton

Publisher:

Published: 2017

Total Pages: 168

ISBN-13: 9781470440527

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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

Locally Analytic Vectors in Representations of Locally $p$-adic Analytic Groups
Locally Analytic Vectors in Representations of Locally $p$-adic Analytic Groups

Author: Matthew J. Emerton

Publisher: American Mathematical Soc.

Published: 2017-07-13

Total Pages: 168

ISBN-13: 0821875620

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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.

p-adic Banach Space Representations
p-adic Banach Space Representations

Author: Dubravka Ban

Publisher: Springer Nature

Published: 2023-02-11

Total Pages: 219

ISBN-13: 3031226844

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This book systematically develops the theory of continuous representations on p-adic Banach spaces. Its purpose is to lay the foundations of the representation theory of reductive p-adic groups on p-adic Banach spaces, explain the duality theory of Schneider and Teitelbaum, and demonstrate its applications to continuous principal series. Written to be accessible to graduate students, the book gives a comprehensive introduction to the necessary tools, including Iwasawa algebras, p-adic measures and distributions, p-adic functional analysis, reductive groups, and smooth and algebraic representations. Part 1 culminates with the duality between Banach space representations and Iwasawa modules. This duality is applied in Part 2 for studying the intertwining operators and reducibility of the continuous principal series on p-adic Banach spaces. This monograph is intended to serve both as a reference book and as an introductory text for graduate students and researchers entering the area.

Automorphic Forms and Galois Representations
Automorphic Forms and Galois Representations

Author: Fred Diamond

Publisher: Cambridge University Press

Published: 2014-10-16

Total Pages: 385

ISBN-13: 1107691923

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Part one of a two-volume collection exploring recent developments in number theory related to automorphic forms and Galois representations.

Automorphic Forms and Galois Representations: Volume 1
Automorphic Forms and Galois Representations: Volume 1

Author: Fred Diamond

Publisher: Cambridge University Press

Published: 2014-10-16

Total Pages: 385

ISBN-13: 1316062333

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Automorphic forms and Galois representations have played a central role in the development of modern number theory, with the former coming to prominence via the celebrated Langlands program and Wiles' proof of Fermat's Last Theorem. This two-volume collection arose from the 94th LMS-EPSRC Durham Symposium on 'Automorphic Forms and Galois Representations' in July 2011, the aim of which was to explore recent developments in this area. The expository articles and research papers across the two volumes reflect recent interest in p-adic methods in number theory and representation theory, as well as recent progress on topics from anabelian geometry to p-adic Hodge theory and the Langlands program. The topics covered in volume one include the Shafarevich Conjecture, effective local Langlands correspondence, p-adic L-functions, the fundamental lemma, and other topics of contemporary interest.

Cohomology of Arithmetic Groups
Cohomology of Arithmetic Groups

Author: James W. Cogdell

Publisher: Springer

Published: 2018-08-18

Total Pages: 304

ISBN-13: 3319955497

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This book discusses the mathematical interests of Joachim Schwermer, who throughout his career has focused on the cohomology of arithmetic groups, automorphic forms and the geometry of arithmetic manifolds. To mark his 66th birthday, the editors brought together mathematical experts to offer an overview of the current state of research in these and related areas. The result is this book, with contributions ranging from topology to arithmetic. It probes the relation between cohomology of arithmetic groups and automorphic forms and their L-functions, and spans the range from classical Bianchi groups to the theory of Shimura varieties. It is a valuable reference for both experts in the fields and for graduate students and postdocs wanting to discover where the current frontiers lie.

Modern Trends in Algebra and Representation Theory
Modern Trends in Algebra and Representation Theory

Author: David Jordan

Publisher: Cambridge University Press

Published: 2023-08-17

Total Pages: 407

ISBN-13: 1009097350

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Expanding upon the material delivered during the LMS Autumn Algebra School 2020, this volume reflects the fruitful connections between different aspects of representation theory. Each survey article addresses a specific subject from a modern angle, beginning with an exploration of the representation theory of associative algebras, followed by the coverage of important developments in Lie theory in the past two decades, before the final sections introduce the reader to three strikingly different aspects of group theory. Written at a level suitable for graduate students and researchers in related fields, this book provides pure mathematicians with a springboard into the vast and growing literature in each area.