Representation Theory And Harmonic Analysis
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Representation Theory And Harmonic Analysis On Semisimple Lie Groups
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Author : Paul J. Sally (Jr.)
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
Representation Theory And Harmonic Analysis On Semisimple Lie Groups written by Paul J. Sally (Jr.) and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
This book brings together five papers that have been influential in the study of Lie groups. Though published more than 20 years ago, these papers made fundamental contributions that deserve much broader exposure. In addition, the subsequent literature that has subsumed these papers cannot replace the originality and vitality they contain. The editors have provided a brief introduction to each paper, as well as a synopsis of the major developments which have occurred in the area covered by each paper. Included here are the doctoral theses of Arthur, Osborne, and Schmid. Arthur's thesis is closely related to Trombi's paper insofar as both deal with harmonic analysis on real semisimple Lie groups, and, in particular, analysis on the Schwartz space of Harish-Chandra. Arthur's thesis is concerned with the image under the Fourier transform of the Schwartz space of a semisimple Lie group of real rank one, while Trombi's paper provides an expository account of the harmonic analysis associated to the decomposition of the Schwartz space under the regular representation. In his thesis, Osborne extends the Atiyah-Bott fixed point theorem for elliptic complexes to obtain a fixed point formula for complexes that are not elliptic. Schmid proves a generalization of the Borel-Weil theorem concerning an explicit and geometric realization of the irreducible representations of a compact, connected semisimple Lie group. Langlands's fundamental paper provides a classification of irreducible, admissible representations of real reductive Lie groups.
Representation Theory And Complex Analysis
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Author : Michael Cowling
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-02-27
Representation Theory And Complex Analysis written by Michael Cowling and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-27 with Mathematics categories.
Six leading experts lecture on a wide spectrum of recent results on the subject of the title. They present a survey of various interactions between representation theory and harmonic analysis on semisimple groups and symmetric spaces, and recall the concept of amenability. They further illustrate how representation theory is related to quantum computing; and much more. Taken together, this volume provides both a solid reference and deep insights on current research activity.
Representation Theory And Harmonic Analysis
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Author : Ray Alden Kunze
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Representation Theory And Harmonic Analysis written by Ray Alden Kunze and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
This volume stems from a special session on representation theory and harmonic analysis held in honour of Ray Kunze at the 889th meeting of the American Mathematical Society on January 12-15 1994. It is intended for graduate students and research mathematicians interested in topological groups, lie groups and abstract harmonic analysis.
Non Abelian Harmonic Analysis
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Author : Roger E. Howe
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Non Abelian Harmonic Analysis written by Roger E. Howe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book mainly discusses the representation theory of the special linear group 8L(2, 1R), and some applications of this theory. In fact the emphasis is on the applications; the working title of the book while it was being writ ten was "Some Things You Can Do with 8L(2). " Some of the applications are outside representation theory, and some are to representation theory it self. The topics outside representation theory are mostly ones of substantial classical importance (Fourier analysis, Laplace equation, Huyghens' prin ciple, Ergodic theory), while the ones inside representation theory mostly concern themes that have been central to Harish-Chandra's development of harmonic analysis on semisimple groups (his restriction theorem, regularity theorem, character formulas, and asymptotic decay of matrix coefficients and temperedness). We hope this mix of topics appeals to nonspecialists in representation theory by illustrating (without an interminable prolegom ena) how representation theory can offer new perspectives on familiar topics and by offering some insight into some important themes in representation theory itself. Especially, we hope this book popularizes Harish-Chandra's restriction formula, which, besides being basic to his work, is simply a beautiful example of Fourier analysis on Euclidean space. We also hope representation theorists will enjoy seeing examples of how their subject can be used and will be stimulated by some of the viewpoints offered on representation-theoretic issues.
Harmonic Analysis Group Representations Automorphic Forms And Invariant Theory
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Author : Roger Howe
language : en
Publisher: World Scientific
Release Date : 2007
Harmonic Analysis Group Representations Automorphic Forms And Invariant Theory written by Roger Howe and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
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."
Harmonic Analysis On Finite Groups
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Author : Tullio Ceccherini-Silberstein
language : en
Publisher: Cambridge University Press
Release Date : 2008-03-06
Harmonic Analysis On Finite Groups written by Tullio Ceccherini-Silberstein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-03-06 with Mathematics categories.
Starting from a few concrete problems such as random walks on the discrete circle and the finite ultrametric space, this book develops the necessary tools for the asymptotic analysis of these processes. Its topics range from the basic theory needed for students new to this area, to advanced topics such as the theory of Green's algebras, the complete analysis of the random matchings, and a presentation of the presentation theory of the symmetric group. This self-contained, detailed study culminates with case-by-case analyses of the cut-off phenomenon discovered by Persi Diaconis.
Representation Theory And Harmonic Analysis Of Wreath Products Of Finite Groups
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Author : Tullio Ceccherini-Silberstein
language : en
Publisher: Cambridge University Press
Release Date : 2014-01-16
Representation Theory And Harmonic Analysis Of Wreath Products Of Finite Groups written by Tullio Ceccherini-Silberstein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-16 with Mathematics categories.
A self-contained introduction to the representation theory and harmonic analysis of wreath products of finite groups, with examples and exercises.
Harmonic Analysis And Representation Theory For Groups Acting On Homogeneous Trees
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Author : Alessandro Figà-Talamanca
language : en
Publisher: Cambridge University Press
Release Date : 1991
Harmonic Analysis And Representation Theory For Groups Acting On Homogeneous Trees written by Alessandro Figà-Talamanca and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
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.
Aspects Of Representation Theory And Noncommutative Harmonic Analysis
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Author : Jean H Gallier
language : en
Publisher: World Scientific
Release Date : 2025-01-17
Aspects Of Representation Theory And Noncommutative Harmonic Analysis written by Jean H Gallier and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-17 with Mathematics categories.
This book presents the theory of harmonic analysis for noncommutative compact groups. If G is a commutative locally compact group, there is a well-understood theory of harmonic analysis as discussed in Aspects of Harmonic Analysis on Locally Compact Abelian Groups. If G is not commutative, things are a lot tougher. In the special case of a compact group, there is a deep interplay between analysis and representation theory which was first discovered by Hermann Weyl and refined by Andre Weil. This book presents these seminal results of Weyl and Weil.Starting with the basics of representations theory, it presents the famous Peter-Weyl theorems and discusses Fourier analysis on compact groups. This book also introduces the reader to induced representations of locally compact groups, induced representations of G-bundles, and the theory of Gelfand pairs. A special feature is the chapter on equivariant convolutional neural networks (CNNs), a chapter which shows how many of the abstract concepts of representations, analysis on compact groups, Peter-Weyl theorems, Fourier transform, induced representations are used to tackle very practical, modern-day problems.
Representation Theory And Harmonic Analysis Toward The New Century
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Author : Takashi Hashimoto
language : en
Publisher:
Release Date : 2002
Representation Theory And Harmonic Analysis Toward The New Century written by Takashi Hashimoto and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.