Author: Publisher: Academic Press
ISBN: 0080874525
Category : Mathematics
Languages : en
Pages : 475
Book Description
Real Reductive Groups II
Real Reductive Groups II
Author: Publisher: Academic Press
ISBN: 0080874525
Category : Mathematics
Languages : en
Pages : 475
Book Description
Real Reductive Groups II
Harmonic Analysis of Spherical Functions on Real Reductive Groups
Author: Ramesh GangolliPublisher: Springer Science & Business Media
ISBN: 3642729568
Category : Mathematics
Languages : en
Pages : 379
Book Description
Analysis on Symmetric spaces, or more generally, on homogeneous spaces of semisimple Lie groups, is a subject that has undergone a vigorous development in recent years, and has become a central part of contemporary mathematics. This is only to be expected, since homogeneous spaces and group representations arise naturally in diverse contexts ranging from Number theory and Geometry to Particle Physics and Polymer Chemistry. Its explosive growth sometimes makes it difficult to realize that it is actually relatively young as mathematical theories go. The early ideas in the subject (as is the case with many others) go back to Elie Cart an and Hermann Weyl who studied the compact symmetric spaces in the 1930's. However its full development did not begin until the 1950's when Gel'fand and Harish Chandra dared to dream of a theory of representations that included all semisimple Lie groups. Harish-Chandra's theory of spherical functions was essentially complete in the late 1950's, and was to prove to be the forerunner of his monumental work on harmonic analysis on reductive groups that has inspired a whole generation of mathematicians. It is the harmonic analysis of spherical functions on symmetric spaces, that is at the focus of this book. The fundamental questions of harmonic analysis on symmetric spaces involve an interplay of the geometric, analytical, and algebraic aspects of these spaces. They have therefore attracted a great deal of attention, and there have been many excellent expositions of the themes that are characteristic of this subject.
Real Reductive Groups
Author: Nolan R. WallachPublisher:
ISBN:
Category : Lie groups
Languages : en
Pages :
Book Description
Real Reductive Groups I
Author: Nolan R. WallachPublisher: Academic Press
ISBN: 0080874517
Category : Mathematics
Languages : en
Pages : 439
Book Description
Real Reductive Groups I is an introduction to the representation theory of real reductive groups. It is based on courses that the author has given at Rutgers for the past 15 years. It also had its genesis in an attempt of the author to complete a manuscript of the lectures that he gave at the CBMS regional conference at The University of North Carolina at Chapel Hill in June of 1981. This book comprises 10 chapters and begins with some background material as an introduction. The following chapters then discuss elementary representation theory; real reductive groups; the basic theory of (g, K)-modules; the asymptotic behavior of matrix coefficients; The Langlands Classification; a construction of the fundamental series; cusp forms on G; character theory; and unitary representations and (g, K)-cohomology. This book will be of interest to mathematicians and statisticians.
Representations of Algebraic Groups
Author: Jens Carsten JantzenPublisher: American Mathematical Soc.
ISBN: 082184377X
Category : Mathematics
Languages : en
Pages : 594
Book Description
Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.
Representation Theory of Real Reductive Lie Groups
Author: James ArthurPublisher: American Mathematical Soc.
ISBN: 0821843664
Category : Mathematics
Languages : en
Pages : 258
Book Description
"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."--BOOK JACKET.
The Langlands Classification and Irreducible Characters for Real Reductive Groups
Author: J. AdamsPublisher: Springer Science & Business Media
ISBN: 146120383X
Category : Mathematics
Languages : en
Pages : 331
Book Description
This monograph explores the geometry of the local Langlands conjecture. The conjecture predicts a parametrizations of the irreducible representations of a reductive algebraic group over a local field in terms of the complex dual group and the Weil-Deligne group. For p-adic fields, this conjecture has not been proved; but it has been refined to a detailed collection of (conjectural) relationships between p-adic representation theory and geometry on the space of p-adic representation theory and geometry on the space of p-adic Langlands parameters. This book provides and introduction to some modern geometric methods in representation theory. It is addressed to graduate students and research workers in representation theory and in automorphic forms.
Character Identities in the Twisted Endoscopy of Real Reductive Groups
Author: Paul MezoPublisher: American Mathematical Soc.
ISBN: 0821875655
Category : Mathematics
Languages : en
Pages : 106
Book Description
Suppose $G$ is a real reductive algebraic group, $\theta$ is an automorphism of $G$, and $\omega$ is a quasicharacter of the group of real points $G(\mathbf{R})$. Under some additional assumptions, the theory of twisted endoscopy associates to this triple real reductive groups $H$. The Local Langlands Correspondence partitions the admissible representations of $H(\mathbf{R})$ and $G(\mathbf{R})$ into $L$-packets. The author proves twisted character identities between $L$-packets of $H(\mathbf{R})$ and $G(\mathbf{R})$ comprised of essential discrete series or limits of discrete series.
Representations of Reductive Groups
Author: Roger W. CarterPublisher: Cambridge University Press
ISBN: 0521643252
Category : Mathematics
Languages : en
Pages : 203
Book Description
This volume provides a very accessible introduction to the representation theory of reductive algebraic groups.
Representations of Reductive Groups
Author: Avraham AizenbudPublisher: American Mathematical Soc.
ISBN: 1470442841
Category : Mathematics
Languages : en
Pages : 466
Book Description
This volume contains the proceedings of the Conference on Representation Theory and Algebraic Geometry, held in honor of Joseph Bernstein, from June 11–16, 2017, at the Weizmann Institute of Science and The Hebrew University of Jerusalem. The topics reflect the decisive and diverse impact of Bernstein on representation theory in its broadest scope. The themes include representations of p -adic groups and Hecke algebras in all characteristics, representations of real groups and supergroups, theta correspondence, and automorphic forms.