[PDF] A Satake Compactification Of Some Locally Symmetric Spaces For Sl3r eBook

Author : Y. Guivarc'h
Publisher : Boston : Birkhäuser
Page : 284 pages
File Size : 42,19 MB
Release : 1998
Category : Compactifications
ISBN : 9783764338992

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Investigates the interrelationships of the perspectives on the compactifications that have been developed in the contexts of representation theory, geometry, and random walks, with a view to resolving the differences. Defines and analyzes in detail the Martin version, describes new geometric versions defined in terms of the Tits building, and looks at the well known isomorphism between the Satake and the Furstenberg versions. Annotation copyrighted by Book News, Inc., Portland, OR

Author : Jean-Philippe Anker
Publisher : Springer Science & Business Media
Page : 216 pages
File Size : 36,53 MB
Release : 2006-02-25
Category : Mathematics
ISBN : 081764430X

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* Focuses on two fundamental questions related to semisimple Lie groups: the geometry of Riemannian symmetric spaces and their compactifications, and branching laws for unitary representations * Wide applications of compactification techniques * Concrete examples and relevant exercises engage the reader * Knowledge of basic representation theory of Lie groups, semisimple Lie groups and symmetric spaces is required

Author : Lizhen Ji
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 37,26 MB
Release : 2008
Category : Mathematics
ISBN : 0821848666

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In one guise or another, many mathematicians are familiar with certain arithmetic groups, such as $\mathbf{Z}$ or $\textrm{SL}(n, \mathbf{Z})$. Yet, many applications of arithmetic groups and many connections to other subjects within mathematics are less well known. Indeed, arithmetic groups admit many natural and important generalizations. The purpose of this expository book is to explain, through some brief and informal comments and extensive references, what arithmetic groups and their generalizations are, why they are important to study, and how they can be understood and applied to many fields, such as analysis, geometry, topology, number theory, representation theory, and algebraic geometry. It is hoped that such an overview will shed a light on the important role played by arithmetic groups in modern mathematics. Titles in this series are co-published with International Press, Cambridge, MA.Table of Contents: Introduction; General comments on references; Examples of basic arithmetic groups; General arithmetic subgroups and locally symmetric spaces; Discrete subgroups of Lie groups and arithmeticity of lattices in Lie groups; Different completions of $\mathbb{Q}$ and $S$-arithmetic groups over number fields; Global fields and $S$-arithmetic groups over function fields; Finiteness properties of arithmetic and $S$-arithmetic groups; Symmetric spaces, Bruhat-Tits buildings and their arithmetic quotients; Compactifications of locally symmetric spaces; Rigidity of locally symmetric spaces; Automorphic forms and automorphic representations for general arithmetic groups; Cohomology of arithmetic groups; $K$-groups of rings of integers and $K$-groups of group rings; Locally homogeneous manifolds and period domains; Non-cofinite discrete groups, geometrically finite groups; Large scale geometry of discrete groups; Tree lattices; Hyperbolic groups; Mapping class groups and outer automorphism groups of free groups; Outer automorphism group of free groups and the outer spaces; References; Index. Review from Mathematical Reviews: ...the author deserves credit for having done the tremendous job of encompassing every aspect of arithmetic groups visible in today's mathematics in a systematic manner; the book should be an important guide for some time to come.(AMSIP/43.

Author : Gestur Olafsson
Publisher : Academic Press
Page : 303 pages
File Size : 28,54 MB
Release : 1996-09-11
Category : Mathematics
ISBN : 0080528724

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This book is intended to introduce researchers and graduate students to the concepts of causal symmetric spaces. To date, results of recent studies considered standard by specialists have not been widely published. This book seeks to bring this information to students and researchers in geometry and analysis on causal symmetric spaces. Includes the newest results in harmonic analysis including Spherical functions on ordered symmetric space and the holmorphic discrete series and Hardy spaces on compactly casual symmetric spaces Deals with the infinitesimal situation, coverings of symmetric spaces, classification of causal symmetric pairs and invariant cone fields Presents basic geometric properties of semi-simple symmetric spaces Includes appendices on Lie algebras and Lie groups, Bounded symmetric domains (Cayley transforms), Antiholomorphic Involutions on Bounded Domains and Para-Hermitian Symmetric Spaces

Author : Denis Auroux
Publisher : Birkhäuser
Page : 368 pages
File Size : 26,82 MB
Release : 2017-07-27
Category : Mathematics
ISBN : 3319599399

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This volume is a tribute to Maxim Kontsevich, one of the most original and influential mathematicians of our time. Maxim’s vision has inspired major developments in many areas of mathematics, ranging all the way from probability theory to motives over finite fields, and has brought forth a paradigm shift at the interface of modern geometry and mathematical physics. Many of his papers have opened completely new directions of research and led to the solutions of many classical problems. This book collects papers by leading experts currently engaged in research on topics close to Maxim’s heart. Contributors: S. Donaldson A. Goncharov D. Kaledin M. Kapranov A. Kapustin L. Katzarkov A. Noll P. Pandit S. Pimenov J. Ren P. Seidel C. Simpson Y. Soibelman R. Thorngren