ORBITAL INTEGRALS ON  REDUCTIVE LIE GROUPS  AND THEIR ALGEBRAS

ORBITAL INTEGRALS ON REDUCTIVE LIE GROUPS AND THEIR ALGEBRAS by Francisco Bulnes Orbital Integrals on Reductive Lie Groups and Their Algebras http://dx.doi.org/10.5772/56023 by Francisco Bulnes Published by InTech Janeza Trdine 9, 51000 Rijeka, Croatia Copyright © 2013 InTech All chapters are Open Access distributed under the Creative Commons Attribution 3.0 license, which allows users to download, copy and build upon published articles even for commercial purposes, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications.After this work has been published by InTech, authors have the right to republish it, in whole or part, in any publication of which they are the author, and to make other personal use of the work. Any republication, referencing or personal use of the work must explicitly identify the original source. Notice Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published chapters. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideascontained inthebook. Publishing Process Manager Danijela Duric Typesetting www.pantype.com Cover InTech Design Team First published March, 2013 Printed in Croatia A free online edition of this book is available at www.intechopen.com Additional hard copies can be obtained from orders@intechopen.com Orbital Integrals on Reductive Lie Groups and Their Algebras, by Francisco Bulnes p. cm. ISBN 978-953-51-1007-1 Contents Preface IX Chapter 1 Introduction 1 Chapter 2 Chapter 3 Integrals, Functional and Special Functions on Lie Groups and Lie Algebras 9 Orbital Integrals on Reductive Lie Groups 21 Chapter 4 Orbital Integrals on Reductive Lie Algebras 35 Chapter 5 Integral Transforms on Lie Groups and Lie Algebras 47 Chapter 6 Intertwinning Operators 67 Chapter 7 Some Examples of Orbital Integrals into Representation Theory on Field Theory and Integral Geometry 75 Chapter 8 Orbital Integrals on Cuspidal Forms 89 Chapter 9 Some Applications in the Study of Harmonic Analysis 97 Chapter 10 Cohomological Induction and Securing of Generalized G-Modules by G(w)-Orbits to Infinite Dimensional Representations of Lie Groups 111 Appendix A Integral Formulas on Canonical p-Pairs 123 Appendix B Regularity on a Lie Algebra 127 Appendix C Some Elements of the Asymptotic Behavior of the Matrix Coefficients 141 ... - tailieumienphi.vn