Harmonic Analysis And Representation Theory For Groups Acting On Homogenous Trees

Author : Alessandro Figá-Talamanca,Claudio Nebbia
Publisher : Cambridge University Press
Page : 165 pages
File Size : 54,7 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 : Anonim
Publisher : Unknown
Page : 164 pages
File Size : 41,5 Mb
Release : 1991
Category : Trees (Graph theory)
ISBN : 1107366712

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Harmonic Analysis and Representation Theory for Groups Acting on Homogenous Trees by Anonim Pdf

These notes treat in full detail the theory of representations of the group of automorphisms of a homogeneous tree.

Author : Alessandro Figà-Talamanca
Publisher : Unknown
Page : 163 pages
File Size : 54,8 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 110736180X

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Harmonic Analysis and Representation Theory for Groups Acting on Homogenous Trees by Alessandro Figà-Talamanca Pdf

These notes treat in full detail the theory of representations of the group of automorphisms of a homogeneous tree.

Author : Alessandro Figá-Talamanca,Claudio Nebbia
Publisher : Cambridge University Press
Page : 0 pages
File Size : 40,7 Mb
Release : 1991-06-28
Category : Mathematics
ISBN : 0521424445

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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 : Paul Sally,David A. Vogan
Publisher : American Mathematical Soc.
Page : 350 pages
File Size : 51,9 Mb
Release : 1989
Category : Mathematics
ISBN : 9780821815267

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Representation Theory and Harmonic Analysis on Semisimple Lie Groups by Paul Sally,David A. Vogan Pdf

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.

Author : Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli
Publisher : Cambridge University Press
Page : 177 pages
File Size : 46,8 Mb
Release : 2014-01-16
Category : Mathematics
ISBN : 9781107729919

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Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups by Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli Pdf

This book presents an introduction to the representation theory of wreath products of finite groups and harmonic analysis on the corresponding homogeneous spaces. The reader will find a detailed description of the theory of induced representations and Clifford theory, focusing on a general formulation of the little group method. This provides essential tools for the determination of all irreducible representations of wreath products of finite groups. The exposition also includes a detailed harmonic analysis of the finite lamplighter groups, the hyperoctahedral groups, and the wreath product of two symmetric groups. This relies on the generalised Johnson scheme, a new construction of finite Gelfand pairs. The exposition is completely self-contained and accessible to anyone with a basic knowledge of representation theory. Plenty of worked examples and several exercises are provided, making this volume an ideal textbook for graduate students. It also represents a useful reference for more experienced researchers.

Author : Alex Lubotzky
Publisher : Springer Science & Business Media
Page : 201 pages
File Size : 55,8 Mb
Release : 2010-02-17
Category : Mathematics
ISBN : 9783034603324

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Discrete Groups, Expanding Graphs and Invariant Measures by Alex Lubotzky Pdf

In the last ?fteen years two seemingly unrelated problems, one in computer science and the other in measure theory, were solved by amazingly similar techniques from representation theory and from analytic number theory. One problem is the - plicit construction of expanding graphs («expanders»). These are highly connected sparse graphs whose existence can be easily demonstrated but whose explicit c- struction turns out to be a dif?cult task. Since expanders serve as basic building blocks for various distributed networks, an explicit construction is highly des- able. The other problem is one posed by Ruziewicz about seventy years ago and studied by Banach [Ba]. It asks whether the Lebesgue measure is the only ?nitely additive measure of total measure one, de?ned on the Lebesgue subsets of the n-dimensional sphere and invariant under all rotations. The two problems seem, at ?rst glance, totally unrelated. It is therefore so- what surprising that both problems were solved using similar methods: initially, Kazhdan’s property (T) from representation theory of semi-simple Lie groups was applied in both cases to achieve partial results, and later on, both problems were solved using the (proved) Ramanujan conjecture from the theory of automorphic forms. The fact that representation theory and automorphic forms have anything to do with these problems is a surprise and a hint as well that the two questions are strongly related.

Author : Charles V. Benton
Publisher : Nova Publishers
Page : 256 pages
File Size : 40,7 Mb
Release : 2004
Category : Mathematics
ISBN : 1590339134

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Trends in Mathematical Physics Research by Charles V. Benton Pdf

Physics and mathematics have always been closely intertwined, with developments in one field frequently inspiring the other. Currently, there are many unsolved problems in physics which will likely require new innovations in mathematical physics. Mathematical physics is concerned with problems in statistical mechanics, atomic and molecular physics, quantum field theory, and, in general, with the mathematical foundations of theoretical physics. This includes such subjects as scattering theory for n bodies, quantum mechanics (both non-relativistic and relativistic), atomic and molecular physics, the existence and properties of the phases of model ferromagnets, the stability of matter, the theory of symmetry and symmetry breaking in quantum field theory (both in general and in concrete models), and mathematical developments in functional analysis and algebra to which such subjects lead. This book presents leading-edge research in this fast-moving field.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 44,8 Mb
Release : 2024-06-29
Category : Electronic
ISBN : 9789814474405

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

Author : Jian-Shu Li
Publisher : World Scientific
Page : 446 pages
File Size : 40,6 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812770783

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

This volume carries the same title as that of an international conference held at the National University of Singapore, 9-11 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.

Author : Alessandro Figà-Talamanca,Tim Steger
Publisher : American Mathematical Soc.
Page : 68 pages
File Size : 40,9 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825945

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Harmonic Analysis for Anisotropic Random Walks on Homogeneous Trees by Alessandro Figà-Talamanca,Tim Steger Pdf

This work presents a detailed study of the anisotropic series representations of the free product group $\mathbf Z/2\mathbf Z\star \cdots \star \mathbf Z/2\mathbf Z$. These representations are infinite dimensional, irreducible, and unitary and can be divided into principal and complementary series. Anisotropic series representations are interesting because, while they are not restricted from any larger continuous group in which the discrete group is a lattice, they nonetheless share many properties of such restrictions. The results of this work are also valid for nonabelian free groups on finitely many generators.

Author : Calvin C. Moore
Publisher : American Mathematical Society(RI)
Page : 488 pages
File Size : 51,7 Mb
Release : 1973
Category : Mathematics
ISBN : STANFORD:36105031376473

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Harmonic Analysis on Homogeneous Spaces by Calvin C. Moore Pdf

Author : Alexander Grigor’yan
Publisher : American Mathematical Soc.
Page : 150 pages
File Size : 51,5 Mb
Release : 2018-08-23
Category : Finite groups
ISBN : 9781470443979

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Introduction to Analysis on Graphs by Alexander Grigor’yan Pdf

A central object of this book is the discrete Laplace operator on finite and infinite graphs. The eigenvalues of the discrete Laplace operator have long been used in graph theory as a convenient tool for understanding the structure of complex graphs. They can also be used in order to estimate the rate of convergence to equilibrium of a random walk (Markov chain) on finite graphs. For infinite graphs, a study of the heat kernel allows to solve the type problem—a problem of deciding whether the random walk is recurrent or transient. This book starts with elementary properties of the eigenvalues on finite graphs, continues with their estimates and applications, and concludes with heat kernel estimates on infinite graphs and their application to the type problem. The book is suitable for beginners in the subject and accessible to undergraduate and graduate students with a background in linear algebra I and analysis I. It is based on a lecture course taught by the author and includes a wide variety of exercises. The book will help the reader to reach a level of understanding sufficient to start pursuing research in this exciting area.

Author : Asim Orhan Barut,Ryszard R?czka
Publisher : World Scientific
Page : 750 pages
File Size : 49,5 Mb
Release : 1986
Category : Mathematics
ISBN : 9971502178

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Theory of Group Representations and Applications by Asim Orhan Barut,Ryszard R?czka Pdf

Lie!algebras - Topological!groups - Lie!groups - Representations - Special!functions - Induced!representations.

Author : Alessandro Figa-Talamanca
Publisher : CRC Press
Page : 164 pages
File Size : 46,9 Mb
Release : 2020-11-26
Category : Mathematics
ISBN : 9781000153293

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Harmonic Analysis on Free Groups by Alessandro Figa-Talamanca Pdf

This book presents an account of recent results on the theory of representations and the harmonic analysis of free groups. It emphasizes the analogy with the theory of representations of noncompact semisimple Lie groups and restricts the focus to a class of irreducible unitary representations.