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.

Author:

Publisher: World Scientific

Published:

Total Pages: 1191

ISBN-13:

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

Author: David Jordan

Publisher: Cambridge University Press

Published: 2023-07-31

Total Pages: 408

ISBN-13: 1009103474

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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.

Advances in Non-Archimedean Analysis
Advances in Non-Archimedean Analysis

Author: Helge Glöckner

Publisher: American Mathematical Soc.

Published: 2016-05-20

Total Pages: 346

ISBN-13: 1470419882

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This volume contains the Proceedings of the 13th International Conference on p-adic Functional Analysis, held from August 12–16, 2014, at the University of Paderborn, Paderborn, Germany. The articles included in this book feature recent developments in various areas of non-Archimedean analysis, non-Archimedean functional analysis, representation theory, number theory, non-Archimedean dynamical systems and applications. Through a combination of new research articles and survey papers, this book provides the reader with an overview of current developments and techniques in non-Archimedean analysis as well as a broad knowledge of some of the sub-areas of this exciting and fast-developing research area.

Non-abelian Fundamental Groups and Iwasawa Theory
Non-abelian Fundamental Groups and Iwasawa Theory

Author: John Coates

Publisher: Cambridge University Press

Published: 2011-12-15

Total Pages: 321

ISBN-13: 1139505653

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This book describes the interaction between several key aspects of Galois theory based on Iwasawa theory, fundamental groups and automorphic forms. These ideas encompass a large portion of mainstream number theory and ramifications that are of interest to graduate students and researchers in number theory, algebraic geometry, topology and physics.

Representation Theory and Harmonic Analysis on Symmetric Spaces
Representation Theory and Harmonic Analysis on Symmetric Spaces

Author: Jens Gerlach Christensen

Publisher: American Mathematical Soc.

Published: 2018-08-27

Total Pages: 330

ISBN-13: 1470440709

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This volume contains the proceedings of the AMS Special Session on Harmonic Analysis, in honor of Gestur Ólafsson's 65th birthday, held on January 4, 2017, in Atlanta, Georgia. The articles in this volume provide fresh perspectives on many different directions within harmonic analysis, highlighting the connections between harmonic analysis and the areas of integral geometry, complex analysis, operator algebras, Lie algebras, special functions, and differential operators. The breadth of contributions highlights the diversity of current research in harmonic analysis and shows that it continues to be a vibrant and fruitful field of inquiry.

$p$-adic Geometry
$p$-adic Geometry

Author: Matthew Baker

Publisher: American Mathematical Soc.

Published: 2008

Total Pages: 220

ISBN-13: 0821844687

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"In recent decades, p-adic geometry and p-adic cohomology theories have become indispensable tools in number theory, algebraic geometry, and the theory of automorphic representations. The Arizona Winter Schoo1 2007, on which the current book is based, was a unique opportunity to introduce graduate students to this subject." "Following invaluable introductions by John Tate and Vladimir Berkovich, two pioneers of non-archimedean geometry, Brian Conrad's chapter introduces the general theory of Tate's rigid analytic spaces, Raynaud's view of them as the generic fibers of formal schemes, and Berkovich spaces. Samit Dasgupta and Jeremy Teitelbaum discuss the p-adic upper half plane as an example of a rigid analytic space and give applications to number theory (modular forms and the p-adic Langlands program). Matthew Baker offers a detailed discussion of the Berkovich projective line and p-adic potential theory on that and more general Berkovich curves. Finally, Kiran Kedlaya discusses theoretical and computational aspects of p-adic cohomology and the zeta functions of varieties. This book will be a welcome addition to the library of any graduate student and researcher who is interested in learning about the techniques of p-adic geometry."--BOOK JACKET.

Automorphic Forms and Galois Representations: Volume 2
Automorphic Forms and Galois Representations: Volume 2

Author: Fred Diamond

Publisher: Cambridge University Press

Published: 2014-10-16

Total Pages: 387

ISBN-13: 1316062341

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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 two include curves and vector bundles in p-adic Hodge theory, associators, Shimura varieties, the birational section conjecture, and other topics of contemporary interest.

Geometry and Dynamics of Groups and Spaces
Geometry and Dynamics of Groups and Spaces

Author: Mikhail Kapranov

Publisher: Springer Science & Business Media

Published: 2008-03-05

Total Pages: 759

ISBN-13: 3764386088

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Alexander Reznikov (1960-2003) was a brilliant and highly original mathematician. This book presents 18 articles by prominent mathematicians and is dedicated to his memory. In addition it contains an influential, so far unpublished manuscript by Reznikov of book length. The book further provides an extensive survey on Kleinian groups in higher dimensions and some articles centering on Reznikov as a person.

Trends in Number Theory
Trends in Number Theory

Author: Fernando Chamizo

Publisher: American Mathematical Soc.

Published: 2015-09-28

Total Pages: 258

ISBN-13: 0821898582

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This volume contains the proceedings of the Fifth Spanish Meeting on Number Theory, held from July 8-12, 2013, at the Universidad de Sevilla, Sevilla, Spain. The articles contained in this book give a panoramic vision of the current research in number theory, both in Spain and abroad. Some of the topics covered in this volume are classical algebraic number theory, arithmetic geometry, and analytic number theory. This book is published in cooperation with Real Sociedad Matemática Española (RSME).