Spherical D Modules And Representations Of Reductive Lie Groups
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Spherical D Modules And Representations Of Reductive Lie Groups
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Author : Frédéric Vincent Bien
language : en
Publisher:
Release Date : 1986
Spherical D Modules And Representations Of Reductive Lie Groups written by Frédéric Vincent Bien and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.
D Modules And Spherical Representations Mn 39
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Author : Frédéric V. Bien
language : en
Publisher: Princeton University Press
Release Date : 2014-07-14
D Modules And Spherical Representations Mn 39 written by Frédéric V. Bien and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.
The theory of D-modules deals with the algebraic aspects of differential equations. These are particularly interesting on homogeneous manifolds, since the infinitesimal action of a Lie algebra consists of differential operators. Hence, it is possible to attach geometric invariants, like the support and the characteristic variety, to representations of Lie groups. By considering D-modules on flag varieties, one obtains a simple classification of all irreducible admissible representations of reductive Lie groups. On the other hand, it is natural to study the representations realized by functions on pseudo-Riemannian symmetric spaces, i.e., spherical representations. The problem is then to describe the spherical representations among all irreducible ones, and to compute their multiplicities. This is the goal of this work, achieved fairly completely at least for the discrete series representations of reductive symmetric spaces. The book provides a general introduction to the theory of D-modules on flag varieties, and it describes spherical D-modules in terms of a cohomological formula. Using microlocalization of representations, the author derives a criterion for irreducibility. The relation between multiplicities and singularities is also discussed at length. Originally published in 1990. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Non Spherical Principal Series Representations Of A Semisimple Lie Group
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Author : Alfred Magnus
language : en
Publisher: American Mathematical Soc.
Release Date : 1979
Non Spherical Principal Series Representations Of A Semisimple Lie Group written by Alfred Magnus 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 1979 with Mathematics categories.
Non-spherical principal series representations of a real semisimple Lie group are studied. These are representations, induced by a one-dimensional representation of a minimal parabolic subgroup, which have a one-dimensional subspace left stable by a maximal compact subgroup of the original group G. Necessary and sufficient conditions for such a representation to be irreducible, or to be cyclic, are found, in terms of parameters determined by certain rank one subgroups of G. A sufficient condition for such a representation to be unitary is found, and the condition is shown to be necessary in the rank one case.
An Introduction To Lie Groups And Lie Algebras
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Author : Alexander A. Kirillov
language : en
Publisher: Cambridge University Press
Release Date : 2008-07-31
An Introduction To Lie Groups And Lie Algebras written by Alexander A. Kirillov 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 2008-07-31 with Mathematics categories.
Contemporary introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples
Representations Of Real Reductive Lie Groups
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Author : David A. Vogan
language : en
Publisher: Birkhauser
Release Date : 1981
Representations Of Real Reductive Lie Groups written by David A. Vogan and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.
Noncompact Lie Groups And Some Of Their Applications
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Author : Elizabeth A. Tanner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Noncompact Lie Groups And Some Of Their Applications written by Elizabeth A. Tanner 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.
During the past two decades representations of noncompact Lie groups and Lie algebras have been studied extensively, and their application to other branches of mathematics and to physical sciences has increased enormously. Several theorems which were proved in the abstract now carry definite mathematical and physical sig nificance. Several physical observations which were not understood before are now explained in terms of models based on new group-theoretical structures such as dy namical groups and Lie supergroups. The workshop was designed to bring together those mathematicians and mathematical physicists who are actively working in this broad spectrum of research and to provide them with the opportunity to present their recent results and to discuss the challenges facing them in the many problems that remain. The objective of the workshop was indeed well achieved. This book contains 31 lectures presented by invited participants attending the NATO Advanced Research Workshop held in San Antonio, Texas, during the week of January 3-8, 1993. The introductory article by the editors provides a brief review of the concepts underlying these lectures (cited by author [*]) and mentions some of their applications. The articles in the book are grouped under the following general headings: Lie groups and Lie algebras, Lie superalgebras and Lie supergroups, and Quantum groups, and are arranged in the order in which they are cited in the introductory article. We are very thankful to Dr.
Representation Theory Of Real Reductive Lie Groups
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Author : Wilfried Schmid, James Arthur, Peter E. Trapa
language : en
Publisher: American Mathematical Soc.
Release Date : 2008-10-17
Representation Theory Of Real Reductive Lie Groups written by Wilfried Schmid, James Arthur, Peter E. Trapa 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 2008-10-17 with Representations of Lie groups categories.
The representation theory of real reductive groups is still incomplete, in spite of much progress made thus far. The papers in this volume were presented at the AMS-IMS-SIAM Joint Summer Research Conference ``Representation Theory of Real Reductive Lie Groups'' held in Snowbird, Utah in June 2006, with the aim of elucidating the problems that remain, as well as explaining what tools have recently become available to solve them. They represent a significant improvement in the exposition of some of the most important (and often least accessible) aspects of the literature. This volume will be of interest to graduate students working in the harmonic analysis and representation theory of Lie groups. It will also appeal to experts working in closely related fields.
Representation Theory And Noncommutative Harmonic Analysis Ii
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Author : A.A. Kirillov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Representation Theory And Noncommutative Harmonic Analysis Ii written by A.A. Kirillov 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 2013-03-09 with Mathematics categories.
Two surveys introducing readers to the subjects of harmonic analysis on semi-simple spaces and group theoretical methods, and preparing them for the study of more specialised literature. This book will be very useful to students and researchers in mathematics, theoretical physics and those chemists dealing with quantum systems.
Algebraic Analysis
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Author : Masaki Kashiwara
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Algebraic Analysis written by Masaki Kashiwara and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Algebraic Analysis: Papers Dedicated to Professor Mikio Sato on the Occasion of his 60th Birthday, Volume II is a collection of research papers on algebraic analysis and related topics in honor to Professor Mikio Sato’s 60th birthday. This volume is divided into 29 chapters and starts with research works concerning the fundamentals of KP equations, strings, Schottky problem, and the applications of transformation theory for nonlinear integrable systems to linear prediction problems and isospectral deformations,. The subsequent chapters contain papers on the approach to nonlinear integrable systems, the Hodge numbers, the stochastic different equation for the multi-dimensional weakly stationary process, and a method of harmonic analysis on semisimple symmetric spaces. These topics are followed by studies on the quantization of extended vortices, moduli space for Fuchsian groups, microfunctions for boundary value problems, and the issues of multi-dimensional integrable systems. The remaining chapters explore the practical aspects of pseudodifferential operators in hyperfunction theory, the elliptic solitons, and Carlson’s theorem for holomorphic functions. This book will prove useful to mathematicians and advance mathematics students.
Geometry And Representation Theory Of Real And P Adic Groups
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Author : Juan Tirao
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometry And Representation Theory Of Real And P Adic Groups written by Juan Tirao 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.
The representation theory of Lie groups plays a central role in both clas sical and recent developments in many parts of mathematics and physics. In August, 1995, the Fifth Workshop on Representation Theory of Lie Groups and its Applications took place at the Universidad Nacional de Cordoba in Argentina. Organized by Joseph Wolf, Nolan Wallach, Roberto Miatello, Juan Tirao, and Jorge Vargas, the workshop offered expository courses on current research, and individual lectures on more specialized topics. The present vol ume reflects the dual character of the workshop. Many of the articles will be accessible to graduate students and others entering the field. Here is a rough outline of the mathematical content. (The editors beg the indulgence of the readers for any lapses in this preface in the high standards of historical and mathematical accuracy that were imposed on the authors of the articles. ) Connections between flag varieties and representation theory for real re ductive groups have been studied for almost fifty years, from the work of Gelfand and Naimark on principal series representations to that of Beilinson and Bernstein on localization. The article of Wolf provides a detailed introduc tion to the analytic side of these developments. He describes the construction of standard tempered representations in terms of square-integrable partially harmonic forms (on certain real group orbits on a flag variety), and outlines the ingredients in the Plancherel formula. Finally, he describes recent work on the complex geometry of real group orbits on partial flag varieties.