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Geometry And Representation Theory Of Real And P Adic Groups

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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.

Geometry And Representation Theory Of Real And P Adic Groups

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Author : Juan Tirao
language : en
Publisher:
Release Date : 1997-11-18

Geometry And Representation Theory Of Real And P Adic Groups written by Juan Tirao and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-11-18 with categories.

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 : 1998

P Adic Analysis And Mathematical Physics

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Author : Vasili? Sergeevich Vladimirov
language : en
Publisher: World Scientific
Release Date : 1994

P Adic Analysis And Mathematical Physics written by Vasili? Sergeevich Vladimirov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Science categories.

p-adic numbers play a very important role in modern number theory, algebraic geometry and representation theory. Lately p-adic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the non-Archimedean geometry of space-time at small distances.This is the first book to deal with applications of p-adic numbers in theoretical and mathematical physics. It gives an elementary and thoroughly written introduction to p-adic numbers and p-adic analysis with great numbers of examples as well as applications of p-adic numbers in classical mechanics, dynamical systems, quantum mechanics, statistical physics, quantum field theory and string theory.

Elements Of The Representation Theory Of The Jacobi Group

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Author : Rolf Berndt
language : en
Publisher: Springer Science & Business Media
Release Date : 1998

Elements Of The Representation Theory Of The Jacobi Group written by Rolf Berndt 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 1998 with Mathematics categories.

The Jacobi group is a semidirect product of a symplectic group with a Heisenberg group. It is an important example for a non-reductive group and sets the frame within which to treat theta functions as well as elliptic functions - in particular, the universal elliptic curve. This text gathers for the first time material from the representation theory of this group in both local (archimedean and non-archimedean) cases and in the global number field case. Via a bridge to Waldspurger's theory for the metaplectic group, complete classification theorems for irreducible representations are obtained. Further topics include differential operators, Whittaker models, Hecke operators, spherical representations and theta functions. The global theory is aimed at the correspondence between automorphic representations and Jacobi forms. This volume is thus a complement to the seminal book on Jacobi forms by M. Eichler and D. Zagier. Incorporating results of the authors' original research, this exposition is meant for researchers and graduate students interested in algebraic groups and number theory, in particular, modular and automorphic forms.

Calculus Of Variations And Geometric Evolution Problems

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Author : F. Bethuel
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-10-19

Calculus Of Variations And Geometric Evolution Problems written by F. Bethuel 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 1999-10-19 with Mathematics categories.

The international summer school on Calculus of Variations and Geometric Evolution Problems was held at Cetraro, Italy, 1996. The contributions to this volume reflect quite closely the lectures given at Cetraro which have provided an image of a fairly broad field in analysis where in recent years we have seen many important contributions. Among the topics treated in the courses were variational methods for Ginzburg-Landau equations, variational models for microstructure and phase transitions, a variational treatment of the Plateau problem for surfaces of prescribed mean curvature in Riemannian manifolds - both from the classical point of view and in the setting of geometric measure theory.

Representation Theory Of Lie Groups

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Author : Jeffrey Adams, David Vogan
language : en
Publisher: American Mathematical Soc.
Release Date : 2000-01-25

Representation Theory Of Lie Groups written by Jeffrey Adams, David Vogan 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 2000-01-25 with Mathematics categories.

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.

The Langlands Classification And Irreducible Characters For Real Reductive Groups

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Author : J. Adams
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

The Langlands Classification And Irreducible Characters For Real Reductive Groups written by J. Adams 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.

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.

Introduction To Vertex Operator Algebras And Their Representations

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Author : James Lepowsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2004

Introduction To Vertex Operator Algebras And Their Representations written by James Lepowsky 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 2004 with Mathematics categories.

* Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples. * Begins with a detailed presentation of the theoretical foundations and proceeds to a range of applications. * Includes a number of new, original results and brings fresh perspective to important works of many other researchers in algebra, lie theory, representation theory, string theory, quantum field theory, and other areas of math and physics.

On The Topology Of Isolated Singularities In Analytic Spaces

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Author : José Seade
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-11-18

On The Topology Of Isolated Singularities In Analytic Spaces written by José Seade 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 2005-11-18 with Mathematics categories.

This book has been awarded the Ferran Sunyer i Balaguer 2005 prize. The aim of this book is to give an overview of selected topics on the topology of real and complex isolated singularities, with emphasis on its relations to other branches of geometry and topology. The first chapters are mostly devoted to complex singularities and a myriad of results spread in a vast literature, which are presented here in a unified way, accessible to non-specialists. Among the topics are the fibration theorems of Milnor; the relation with 3-dimensional Lie groups; exotic spheres; spin structures and 3-manifold invariants; the geometry of quadrics and Arnold's theorem which states that the complex projective plane modulo conjugation is the 4-sphere. The second part of the book studies pioneer work about real analytic singularities which arise from the topological and geometric study of holomorphic vector fields and foliations. In the low dimensional case these turn out to be related to fibred links in the 3-sphere defined by meromorphic functions. This provides new methods for constructing manifolds equipped with a rich geometry. The book is largely self-contained and serves a wide audience of graduate students, mathematicians and researchers interested in geometry and topology.

Geometry And Representation Theory Of Real And P Adic Groups

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