Harmonic Analysis Group Representations Automorphic Forms And Invariant Theory

Author : Roger Howe,Jian-Shu Li
Publisher : World Scientific
Page : 446 pages
File Size : 41,8 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812770790

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Harmonic Analysis, Group Representations, Automorphic Forms, and Invariant Theory by Roger Howe,Jian-Shu Li Pdf

This volume carries the same title as that of an international conference held at the National University of Singapore, 9OCo11 January 2006 on the occasion of Roger E. Howe''s 60th birthday. Authored by leading members of the Lie theory community, these contributions, expanded from invited lectures given at the conference, are a fitting tribute to the originality, depth and influence of Howe''s mathematical work. The range and diversity of the topics will appeal to a broad audience of research mathematicians and graduate students interested in symmetry and its profound applications. Sample Chapter(s). Foreword (21 KB). Chapter 1: The Theta Correspondence Over R (342 KB). Contents: The Theta Correspondence over R (J Adams); The Heisenberg Group, SL (3, R), and Rigidity (A iap et al.); Pfaffians and Strategies for Integer Choice Games (R Evans & N Wallach); When is an L -Function Non-Vanishing in Part of the Critical Strip? (S Gelbart); Cohomological Automorphic Forms on Unitary Groups, II: Period Relations and Values of L -Functions (M Harris); The Inversion Formula and Holomorphic Extension of the Minimal Representation of the Conformal Group (T Kobayashi & G Mano); Classification des S(r)ries Discr tes pour Certains Groupes Classiques p- Adiques (C Moeglin); Some Algebras of Essentially Compact Distributions of a Reductive p -Adic Group (A Moy & M Tadic); Annihilators of Generalized Verma Modules of the Scalar Type for Classical Lie Algebras (T Oshima); Branching to a Maximal Compact Subgroup (D A Vogan, Jr.); Small Semisimple Subalgebras of Semisimple Lie Algebras (J F Willenbring & G J Zuckerman). Readership: Graduate students and research mathematicians in harmonic analysis, group representations, automorphic forms and invariant theory."

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 41,7 Mb
Release : 2024-06-27
Category : Electronic
ISBN : 9789814474405

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Harmonic Analysis, Group Representations, Automorphic Forms and Invariant Theory by Anonim Pdf

Author : D. Gurarie
Publisher : Elsevier
Page : 452 pages
File Size : 40,7 Mb
Release : 1992-05-18
Category : Mathematics
ISBN : 0080872859

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Symmetries and Laplacians by D. Gurarie Pdf

Designed as an introduction to harmonic analysis and group representations, this book covers a wide range of topics rather than delving deeply into any particular one. In the words of H. Weyl ...it is primarily meant for the humble, who want to learn as new the things set forth therein, rather than for the proud and learned who are already familiar with the subject and merely look for quick and exact information.... The main objective is to introduce the reader to concepts, ideas, results and techniques that evolve around symmetry-groups, representations and Laplacians. More specifically, the main interest concerns geometrical objects and structures {X}, discrete or continuous, that possess sufficiently large symmetry group G, such as regular graphs (Platonic solids), lattices, and symmetric Riemannian manifolds. All such objects have a natural Laplacian &Dgr;, a linear operator on functions over X, invariant under the group action. There are many problems associated with Laplacians on X, such as continuous or discrete-time evolutions, on X, random walks, diffusion processes, and wave-propagation. This book contains sufficient material for a 1 or 2-semester course.

Author : Alessandro Figá-Talamanca,Claudio Nebbia
Publisher : Cambridge University Press
Page : 165 pages
File Size : 54,5 Mb
Release : 1991-06-28
Category : Mathematics
ISBN : 9780521424448

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Harmonic Analysis and Representation Theory for Groups Acting on Homogenous Trees by Alessandro Figá-Talamanca,Claudio Nebbia Pdf

These notes treat in full detail the theory of representations of the group of automorphisms of a homogeneous tree. The unitary irreducible representations are classified in three types: a continuous series of spherical representations; two special representations; and a countable series of cuspidal representations as defined by G.I. Ol'shiankii. Several notable subgroups of the full automorphism group are also considered. The theory of spherical functions as eigenvalues of a Laplace (or Hecke) operator on the tree is used to introduce spherical representations and their restrictions to discrete subgroups. This will be an excellent companion for all researchers into harmonic analysis or representation theory.

Author : Bernhard Krötz,Omer Offen,Eitan Sayag
Publisher : Springer Science & Business Media
Page : 275 pages
File Size : 42,5 Mb
Release : 2011-12-14
Category : Mathematics
ISBN : 9780817648176

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Representation Theory, Complex Analysis, and Integral Geometry by Bernhard Krötz,Omer Offen,Eitan Sayag Pdf

This volume targets graduate students and researchers in the fields of representation theory, automorphic forms, Hecke algebras, harmonic analysis, number theory.

Author : T. N. Bailey
Publisher : American Mathematical Soc.
Page : 490 pages
File Size : 48,8 Mb
Release : 1997
Category : Automorphic forms
ISBN : 9780821806098

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Representation Theory and Automorphic Forms by T. N. Bailey Pdf

The lectures from a course in the representation theory of semi- simple groups, automorphic forms, and the relations between them. The purpose is to help analysts make systematic use of Lie groups in work on harmonic analysis, differential equations, and mathematical physics; and to provide number theorists with the representation-theoretic input to Wiles's proof of Fermat's Last Theorem. Begins with an introductory treatment of structure theory and ends with the current status of functionality. Annotation copyrighted by Book News, Inc., Portland, OR

Author : Yoshinori Hamahata
Publisher : World Scientific
Page : 388 pages
File Size : 51,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814355605

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Geometry and Analysis of Automorphic Forms of Several Variables by Yoshinori Hamahata Pdf

This volume contains contributions of principal speakers of the symposium on geometry and analysis of automorphic forms of several variables, held in September 2009 at Tokyo, Japan, in honor of Takayuki Oda''s 60th birthday. It presents both research and survey articles in the fields that are the main themes of his work. The volume may serve as a guide to developing areas as well as a resource for researchers who seek a broader view and for students who are beginning to explore automorphic form.

Author : Monica Nevins,Peter E. Trapa
Publisher : Birkhäuser
Page : 532 pages
File Size : 47,9 Mb
Release : 2015-12-18
Category : Mathematics
ISBN : 9783319234434

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Representations of Reductive Groups by Monica Nevins,Peter E. Trapa Pdf

Over the last forty years, David Vogan has left an indelible imprint on the representation theory of reductive groups. His groundbreaking ideas have lead to deep advances in the theory of real and p-adic groups, and have forged lasting connections with other subjects, including number theory, automorphic forms, algebraic geometry, and combinatorics. Representations of Reductive Groups is an outgrowth of the conference of the same name, dedicated to David Vogan on his 60th birthday, which took place at MIT on May 19-23, 2014. This volume highlights the depth and breadth of Vogan's influence over the subjects mentioned above, and point to many exciting new directions that remain to be explored. Notably, the first article by McGovern and Trapa offers an overview of Vogan's body of work, placing his ideas in a historical context. Contributors: Pramod N. Achar, Jeffrey D. Adams, Dan Barbasch, Manjul Bhargava, Cédric Bonnafé, Dan Ciubotaru, Meinolf Geck, William Graham, Benedict H. Gross, Xuhua He, Jing-Song Huang, Toshiyuki Kobayashi, Bertram Kostant, Wenjing Li, George Lusztig, Eric Marberg, William M. McGovern, Wilfried Schmid, Kari Vilonen, Diana Shelstad, Peter E. Trapa, David A. Vogan, Jr., Nolan R. Wallach, Xiaoheng Wang, Geordie Williamson

Author : Ellen Elizabeth Eischen,Wee Teck Gan,Aaron Pollack,Zhiwei Yun
Publisher : American Mathematical Society
Page : 199 pages
File Size : 44,6 Mb
Release : 2024-03-26
Category : Mathematics
ISBN : 9781470474928

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Automorphic Forms Beyond $mathrm {GL}_2$ by Ellen Elizabeth Eischen,Wee Teck Gan,Aaron Pollack,Zhiwei Yun Pdf

The Langlands program has been a very active and central field in mathematics ever since its conception over 50 years ago. It connects number theory, representation theory and arithmetic geometry, and other fields in a profound way. There are nevertheless very few expository accounts beyond the GL(2) case. This book features expository accounts of several topics on automorphic forms on higher rank groups, including rationality questions on unitary group, theta lifts and their applications to Arthur's conjectures, quaternionic modular forms, and automorphic forms over functions fields and their applications to inverse Galois problems. It is based on the lecture notes prepared for the twenty-fifth Arizona Winter School on “Automorphic Forms beyond GL(2)”, held March 5–9, 2022, at the University of Arizona in Tucson. The speakers were Ellen Eischen, Wee Teck Gan, Aaron Pollack, and Zhiwei Yun. The exposition of the book is in a style accessible to students entering the field. Advanced graduate students as well as researchers will find this a valuable introduction to various important and very active research areas.

Author : Jim Cogdell,Ju-Lee Kim,Chen-Bo Zhu
Publisher : Birkhäuser
Page : 626 pages
File Size : 42,8 Mb
Release : 2017-10-19
Category : Mathematics
ISBN : 9783319597287

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Representation Theory, Number Theory, and Invariant Theory by Jim Cogdell,Ju-Lee Kim,Chen-Bo Zhu Pdf

This book contains selected papers based on talks given at the "Representation Theory, Number Theory, and Invariant Theory" conference held at Yale University from June 1 to June 5, 2015. The meeting and this resulting volume are in honor of Professor Roger Howe, on the occasion of his 70th birthday, whose work and insights have been deeply influential in the development of these fields. The speakers who contributed to this work include Roger Howe's doctoral students, Roger Howe himself, and other world renowned mathematicians. Topics covered include automorphic forms, invariant theory, representation theory of reductive groups over local fields, and related subjects.

Author : Werner Müller,Sug Woo Shin,Nicolas Templier
Publisher : Springer
Page : 578 pages
File Size : 40,5 Mb
Release : 2016-09-20
Category : Mathematics
ISBN : 9783319414249

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Families of Automorphic Forms and the Trace Formula by Werner Müller,Sug Woo Shin,Nicolas Templier Pdf

Featuring the work of twenty-three internationally-recognized experts, this volume explores the trace formula, spectra of locally symmetric spaces, p-adic families, and other recent techniques from harmonic analysis and representation theory. Each peer-reviewed submission in this volume, based on the Simons Foundation symposium on families of automorphic forms and the trace formula held in Puerto Rico in January-February 2014, is the product of intensive research collaboration by the participants over the course of the seven-day workshop. The goal of each session in the symposium was to bring together researchers with diverse specialties in order to identify key difficulties as well as fruitful approaches being explored in the field. The respective themes were counting cohomological forms, p-adic trace formulas, Hecke fields, slopes of modular forms, and orbital integrals.

Author : Robert S. Doran, Paul J. Sally, Jr., and Loren Spice
Publisher : American Mathematical Soc.
Page : 294 pages
File Size : 46,8 Mb
Release : 2011
Category : Harmonic analysis
ISBN : 9780821874035

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Harmonic Analysis on Reductive, $p$-adic Groups by Robert S. Doran, Paul J. Sally, Jr., and Loren Spice Pdf

Author : Stephen S. Gelbart
Publisher : Princeton University Press
Page : 227 pages
File Size : 41,6 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881611

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Automorphic Forms on Adele Groups. (AM-83), Volume 83 by Stephen S. Gelbart Pdf

This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of Jacquet and Langlands, the author presents new and previously inaccessible results, and systematically develops explicit consequences and connections with the classical theory. The underlying theme is the decomposition of the regular representation of the adele group of GL(2). A detailed proof of the celebrated trace formula of Selberg is included, with a discussion of the possible range of applicability of this formula. Throughout the work the author emphasizes new examples and problems that remain open within the general theory. TABLE OF CONTENTS: 1. The Classical Theory 2. Automorphic Forms and the Decomposition of L2(PSL(2,R) 3. Automorphic Forms as Functions on the Adele Group of GL(2) 4. The Representations of GL(2) over Local and Global Fields 5. Cusp Forms and Representations of the Adele Group of GL(2) 6. Hecke Theory for GL(2) 7. The Construction of a Special Class of Automorphic Forms 8. Eisenstein Series and the Continuous Spectrum 9. The Trace Formula for GL(2) 10. Automorphic Forms on a Quaternion Algebr?

Author : Werner Müller,Sug Woo Shin,Nicolas Templier
Publisher : Springer Nature
Page : 438 pages
File Size : 40,9 Mb
Release : 2021-05-18
Category : Mathematics
ISBN : 9783030685065

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Relative Trace Formulas by Werner Müller,Sug Woo Shin,Nicolas Templier Pdf

A series of three symposia took place on the topic of trace formulas, each with an accompanying proceedings volume. The present volume is the third and final in this series and focuses on relative trace formulas in relation to special values of L-functions, integral representations, arithmetic cycles, theta correspondence and branching laws. The first volume focused on Arthur’s trace formula, and the second volume focused on methods from algebraic geometry and representation theory. The three proceedings volumes have provided a snapshot of some of the current research, in the hope of stimulating further research on these topics. The collegial format of the symposia allowed a homogeneous set of experts to isolate key difficulties going forward and to collectively assess the feasibility of diverse approaches.

Author : Atsushi Ichino,Kartik Prasanna
Publisher : American Mathematical Society
Page : 214 pages
File Size : 53,7 Mb
Release : 2021-02-23
Category : Mathematics
ISBN : 9781470448943

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Periods of Quaternionic Shimura Varieties. I. by Atsushi Ichino,Kartik Prasanna Pdf

This book formulates a new conjecture about quadratic periods of automorphic forms on quaternion algebras, which is an integral refinement of Shimura's algebraicity conjectures on these periods. It also provides a strategy to attack this conjecture by reformulating it in terms of integrality properties of the theta correspondence for quaternionic unitary groups. The methods and constructions of the book are expected to have applications to other problems related to periods, such as the Bloch-Beilinson conjecture about special values of $L$-functions and constructing geometric realizations of Langlands functoriality for automorphic forms on quaternion algebras.