The Penrose Transform And Analytic Cohomology In Representation Theory

Author : Michael G. Eastwood
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 51,9 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821851760

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The Penrose Transform and Analytic Cohomology in Representation Theory by Michael G. Eastwood Pdf

This book contains refereed papers presented at the AMS-IMS-SIAM Summer Research Conference on the Penrose Transform and Analytic Cohomology in Representation Theory held in the summer of 1992 at Mount Holyoke College. The conference brought together some of the top experts in representation theory and differential geometry. One of the issues explored at the conference was the fact that various integral transforms from representation theory, complex integral geometry, and mathematical physics appear to be instances of the same general construction, which is sometimes called the ``Penrose transform''. There is considerable scope for further research in this area, and this book would serve as an excellent introduction.

Author : Robert J. Baston,Michael G. Eastwood
Publisher : Courier Dover Publications
Page : 257 pages
File Size : 44,7 Mb
Release : 2016-11-16
Category : Mathematics
ISBN : 9780486797298

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The Penrose Transform by Robert J. Baston,Michael G. Eastwood Pdf

"Brings to the reader a huge amount of information, well organized and condensed into less than two hundred pages." — Mathematical Reviews In recent decades twistor theory has become an important focus for students of mathematical physics. Central to twistor theory is the geometrical transform known as the Penrose transform, named for its groundbreaking developer. Geared toward students of physics and mathematics, this advanced text explores the Penrose transform and presupposes no background in twistor theory and a minimal familiarity with representation theory. An introductory chapter sketches the development of the Penrose transform, followed by reviews of Lie algebras and flag manifolds, representation theory and homogeneous vector bundles, and the Weyl group and the Bott-Borel-Weil theorem. Succeeding chapters explore the Penrose transform in terms of the Bernstein-Gelfand-Gelfand resolution, followed by worked examples, constructions of unitary representations, and module structures on cohomology. The treatment concludes with a review of constructions and suggests further avenues for research.

Author : Bernhard Krötz,Omer Offen,Eitan Sayag
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 45,8 Mb
Release : 2011-12-13
Category : Mathematics
ISBN : 9780817648169

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Representation Theory, Complex Analysis, and Integral Geometry by Bernhard Krötz,Omer Offen,Eitan Sayag Pdf

This volume targets graduate students and researchers in the fields of representation theory, automorphic forms, Hecke algebras, harmonic analysis, number theory.

Author : Jeffrey Adams, David Vogan
Publisher : American Mathematical Soc.
Page : 340 pages
File Size : 53,6 Mb
Release : 2015-06-02
Category : Electronic
ISBN : 9781470423148

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Representation Theory of Lie Groups by Jeffrey Adams, David Vogan Pdf

This book contains written versions of the lectures given at the PCMI Graduate Summer School on the representation theory of Lie groups. The volume begins with lectures by A. Knapp and P. Trapa outlining the state of the subject around the year 1975, specifically, the fundamental results of Harish-Chandra on the general structure of infinite-dimensional representations and the Langlands classification. Additional contributions outline developments in four of the most active areas of research over the past 20 years. The clearly written articles present results to date, as follows: R. Zierau and L. Barchini discuss the construction of representations on Dolbeault cohomology spaces. D. Vogan describes the status of the Kirillov-Kostant "philosophy of coadjoint orbits" for unitary representations. K. Vilonen presents recent advances in the Beilinson-Bernstein theory of "localization". And Jian-Shu Li covers Howe's theory of "dual reductive pairs". Each contributor to the volume presents the topics in a unique, comprehensive, and accessible manner geared toward advanced graduate students and researchers. Students should have completed the standard introductory graduate courses for full comprehension of the work. The book would also serve well as a supplementary text for a course on introductory infinite-dimensional representation theory. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

Author : T. Tom Dieck
Publisher : Springer
Page : 317 pages
File Size : 48,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540385172

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Transformation Groups and Representation Theory by T. Tom Dieck Pdf

Author : Ray Alden Kunze
Publisher : American Mathematical Soc.
Page : 270 pages
File Size : 53,5 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821803103

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Representation Theory and Harmonic Analysis by Ray Alden Kunze Pdf

This volume stems from a special session on representation theory and harmonic analysis held in honour of Ray Kunze at the 889th meeting of the American Mathematical Society on January 12-15 1994. It is intended for graduate students and research mathematicians interested in topological groups, lie groups and abstract harmonic analysis.

Author : Semen Grigorʹevich Gindikin
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 41,5 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821803004

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Representation Theory and Analysis on Homogeneous Spaces by Semen Grigorʹevich Gindikin Pdf

A combination of new results and surveys of recent work on representation theory and the harmonic analysis of real and p-adic groups. Among the topics are nilpotent homogeneous spaces, multiplicity formulas for induced representations, and new methods for constructing unitary representations of real reductive groups. The 12 papers are from a conference at Rutgers University, February 1993. No index. Annotation copyright by Book News, Inc., Portland, OR

Author : Mark Green, Phillip Griffiths,Matt Kerr
Publisher : American Mathematical Soc.
Page : 314 pages
File Size : 46,5 Mb
Release : 2013-11-05
Category : Mathematics
ISBN : 9781470410124

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Hodge Theory, Complex Geometry, and Representation Theory by Mark Green, Phillip Griffiths,Matt Kerr Pdf

This monograph presents topics in Hodge theory and representation theory, two of the most active and important areas in contemporary mathematics. The underlying theme is the use of complex geometry to understand the two subjects and their relationships to one another--an approach that is complementary to what is in the literature. Finite-dimensional representation theory and complex geometry enter via the concept of Hodge representations and Hodge domains. Infinite-dimensional representation theory, specifically the discrete series and their limits, enters through the realization of these representations through complex geometry as pioneered by Schmid, and in the subsequent description of automorphic cohomology. For the latter topic, of particular importance is the recent work of Carayol that potentially introduces a new perspective in arithmetic automorphic representation theory. The present work gives a treatment of Carayol's work, and some extensions of it, set in a general complex geometric framework. Additional subjects include a description of the relationship between limiting mixed Hodge structures and the boundary orbit structure of Hodge domains, a general treatment of the correspondence spaces that are used to construct Penrose transforms and selected other topics from the recent literature. A co-publication of the AMS and CBMS.

Author : Monica Nevins,Peter E. Trapa
Publisher : Birkhäuser
Page : 532 pages
File Size : 45,6 Mb
Release : 2015-12-18
Category : Mathematics
ISBN : 9783319234434

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Representations of Reductive Groups by Monica Nevins,Peter E. Trapa Pdf

Over the last forty years, David Vogan has left an indelible imprint on the representation theory of reductive groups. His groundbreaking ideas have lead to deep advances in the theory of real and p-adic groups, and have forged lasting connections with other subjects, including number theory, automorphic forms, algebraic geometry, and combinatorics. Representations of Reductive Groups is an outgrowth of the conference of the same name, dedicated to David Vogan on his 60th birthday, which took place at MIT on May 19-23, 2014. This volume highlights the depth and breadth of Vogan's influence over the subjects mentioned above, and point to many exciting new directions that remain to be explored. Notably, the first article by McGovern and Trapa offers an overview of Vogan's body of work, placing his ideas in a historical context. Contributors: Pramod N. Achar, Jeffrey D. Adams, Dan Barbasch, Manjul Bhargava, Cédric Bonnafé, Dan Ciubotaru, Meinolf Geck, William Graham, Benedict H. Gross, Xuhua He, Jing-Song Huang, Toshiyuki Kobayashi, Bertram Kostant, Wenjing Li, George Lusztig, Eric Marberg, William M. McGovern, Wilfried Schmid, Kari Vilonen, Diana Shelstad, Peter E. Trapa, David A. Vogan, Jr., Nolan R. Wallach, Xiaoheng Wang, Geordie Williamson

Author : Anthony W. Knapp,David A. Vogan Jr.
Publisher : Princeton University Press
Page : 968 pages
File Size : 49,9 Mb
Release : 2016-06-02
Category : Mathematics
ISBN : 9781400883936

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Cohomological Induction and Unitary Representations (PMS-45), Volume 45 by Anthony W. Knapp,David A. Vogan Jr. Pdf

This book offers a systematic treatment--the first in book form--of the development and use of cohomological induction to construct unitary representations. George Mackey introduced induction in 1950 as a real analysis construction for passing from a unitary representation of a closed subgroup of a locally compact group to a unitary representation of the whole group. Later a parallel construction using complex analysis and its associated co-homology theories grew up as a result of work by Borel, Weil, Harish-Chandra, Bott, Langlands, Kostant, and Schmid. Cohomological induction, introduced by Zuckerman, is an algebraic analog that is technically more manageable than the complex-analysis construction and leads to a large repertory of irreducible unitary representations of reductive Lie groups. The book, which is accessible to students beyond the first year of graduate school, will interest mathematicians and physicists who want to learn about and take advantage of the algebraic side of the representation theory of Lie groups. Cohomological Induction and Unitary Representations develops the necessary background in representation theory and includes an introductory chapter of motivation, a thorough treatment of the "translation principle," and four appendices on algebra and analysis.

Author : Martin R. Bridson,Simon Salamon
Publisher : Unknown
Page : 352 pages
File Size : 53,6 Mb
Release : 2002
Category : Mathematics
ISBN : 0198507720

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Invitations to Geometry and Topology by Martin R. Bridson,Simon Salamon Pdf

This volume presents an array of topics that introduce the reader to key ideas in active areas in geometry and topology. The material is presented in a way that both graduate students and researchers should find accessible and enticing. The topics covered range from Morse theory and complex geometry theory to geometric group theory, and are accompanied by exercises that are designed to deepen the reader's understanding and to guide them in exciting directions for future investigation.

Author : Niky Kamran,Peter J. Olver
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 47,8 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821851692

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Lie Algebras, Cohomology, and New Applications to Quantum Mechanics by Niky Kamran,Peter J. Olver Pdf

This volume, which contains a good balance of research and survey papers, presents at look at some of the current development in this extraordinarily rich and vibrant area.

Author : Eric Todd Quinto
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 48,9 Mb
Release : 2001
Category : Mathematics
ISBN : 9780821821350

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Radon Transforms and Tomography by Eric Todd Quinto Pdf

One of the most exciting features of the fields of Radon transforms and tomography is the strong relationship between high-level pure mathematics and applications to areas such as medical imaging and industrial nondestructive evaluation. The proceedings featured in this volume bring together fundamental research articles in the major areas of Radon transforms and tomography. This volume includes expository papers that are of special interest to beginners as well as advanced researchers. Topics include local tomography and wavelets, Lambda tomography and related methods, tomographic methods in RADAR, ultrasound, Radon transforms and differential equations, and the Pompeiu problem. The major themes in Radon transforms and tomography are represented among the research articles. Pure mathematical themes include vector tomography, microlocal analysis, twistor theory, Lie theory, wavelets, harmonic analysis, and distribution theory. The applied articles employ high-quality pure mathematics to solve important practical problems. Effective scanning geometries are developed and tested for a NASA wind tunnel. Algorithms for limited electromagnetic tomographic data and for impedance imaging are developed and tested. Range theorems are proposed to diagnose problems with tomography scanners. Principles are given for the design of X-ray tomography reconstruction algorithms, and numerical examples are provided. This volume offers readers a comprehensive source of fundamental research useful to both beginners and advanced researchers in the fields.

Author : Mark Green,Phillip Griffiths,Matt Kerr
Publisher : American Mathematical Soc.
Page : 145 pages
File Size : 41,6 Mb
Release : 2014-08-12
Category : Mathematics
ISBN : 9780821898574

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Special Values of Automorphic Cohomology Classes by Mark Green,Phillip Griffiths,Matt Kerr Pdf

The authors study the complex geometry and coherent cohomology of nonclassical Mumford-Tate domains and their quotients by discrete groups. Their focus throughout is on the domains which occur as open -orbits in the flag varieties for and , regarded as classifying spaces for Hodge structures of weight three. In the context provided by these basic examples, the authors formulate and illustrate the general method by which correspondence spaces give rise to Penrose transforms between the cohomologies of distinct such orbits with coefficients in homogeneous line bundles.

Author : Gen Komatsu,Masatake Kuranishi
Publisher : Springer Science & Business Media
Page : 322 pages
File Size : 42,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461221661

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Analysis and Geometry in Several Complex Variables by Gen Komatsu,Masatake Kuranishi Pdf

This volume consists of a collection of articles for the proceedings of the 40th Taniguchi Symposium Analysis and Geometry in Several Complex Variables held in Katata, Japan, on June 23-28, 1997. Since the inhomogeneous Cauchy-Riemann equation was introduced in the study of Complex Analysis of Several Variables, there has been strong interaction between Complex Analysis and Real Analysis, in particular, the theory of Partial Differential Equations. Problems in Complex Anal ysis stimulate the development of the PDE theory which subsequently can be applied to Complex Analysis. This interaction involves Differen tial Geometry, for instance, via the CR structure modeled on the induced structure on the boundary of a complex manifold. Such structures are naturally related to the PDE theory. Differential Geometric formalisms are efficiently used in settling problems in Complex Analysis and the results enrich the theory of Differential Geometry. This volume focuses on the most recent developments in this inter action, including links with other fields such as Algebraic Geometry and Theoretical Physics. Written by participants in the Symposium, this vol ume treats various aspects of CR geometry and the Bergman kernel/ pro jection, together with other major subjects in modern Complex Analysis. We hope that this volume will serve as a resource for all who are interested in the new trends in this area. We would like to express our gratitude to the Taniguchi Foundation for generous financial support and hospitality. We would also like to thank Professor Kiyosi Ito who coordinated the organization of the symposium.