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Representation Theory And Number Theory In Connection With The Local Langlands Conjecture
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Book Synopsis Representation Theory and Number Theory in Connection with the Local Langlands Conjecture by : Jürgen Ritter
Download or read book Representation Theory and Number Theory in Connection with the Local Langlands Conjecture written by Jürgen Ritter and published by American Mathematical Soc.. This book was released on 1989 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Langlands Program summarizes those parts of mathematical research belonging to the representation theory of reductive groups and to class field theory. These two topics are connected by the vision that, roughly speaking, the irreducible representations of the general linear group may well serve as parameters for the description of all number fields. In the local case, the base field is a given $p$-adic field $K$ and the extension theory of $K$ is seen as determined by the irreducible representations of the absolute Galois group $G_K$ of $K$. Great progress has been made in establishing correspondence between the supercuspidal representations of $GL(n,K)$ and those irreducible representations of $G_K$ whose degrees divide $n$. Despite these advances, no book or paper has presented the different methods used or even collected known results. This volume contains the proceedings of the conference ``Representation Theory and Number Theory in Connection with the Local Langlands Conjecture,'' held in December 1985 at the University of Augsburg. The program of the conference was divided into two parts: (i) the representation theory of local division algebras and local Galois groups, and the Langlands conjecture in the tame case; and (ii) new results, such as the case $n=p$, the matching theorem, principal orders, tame Deligne representations, classification of representations of $GL(n)$, and the numerical Langlands conjecture. The collection of papers in this volume provides an excellent account of the current state of the local Langlands Program.
Book Synopsis The Local Langlands Conjecture for GL(2) by : Colin J. Bushnell
Download or read book The Local Langlands Conjecture for GL(2) written by Colin J. Bushnell and published by Springer Science & Business Media. This book was released on 2006-08-29 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Local Langlands Conjecture for GL(2) contributes an unprecedented text to the so-called Langlands theory. It is an ambitious research program of already 40 years and gives a complete and self-contained proof of the Langlands conjecture in the case n=2. It is aimed at graduate students and at researchers in related fields. It presupposes no special knowledge beyond the beginnings of the representation theory of finite groups and the structure theory of local fields.
Book Synopsis Langlands Correspondence for Loop Groups by : Edward Frenkel
Download or read book Langlands Correspondence for Loop Groups written by Edward Frenkel and published by Cambridge University Press. This book was released on 2007-06-28 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first account of local geometric Langlands Correspondence, a new area of mathematical physics developed by the author.
Book Synopsis The Geometry and Cohomology of Some Simple Shimura Varieties. (AM-151) by : Michael Harris
Download or read book The Geometry and Cohomology of Some Simple Shimura Varieties. (AM-151) written by Michael Harris and published by Princeton University Press. This book was released on 2001-11-04 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims first to prove the local Langlands conjecture for GLn over a p-adic field and, second, to identify the action of the decomposition group at a prime of bad reduction on the l-adic cohomology of the "simple" Shimura varieties. These two problems go hand in hand. The results represent a major advance in algebraic number theory, finally proving the conjecture first proposed in Langlands's 1969 Washington lecture as a non-abelian generalization of local class field theory. The local Langlands conjecture for GLn(K), where K is a p-adic field, asserts the existence of a correspondence, with certain formal properties, relating n-dimensional representations of the Galois group of K with the representation theory of the locally compact group GLn(K). This book constructs a candidate for such a local Langlands correspondence on the vanishing cycles attached to the bad reduction over the integer ring of K of a certain family of Shimura varieties. And it proves that this is roughly compatible with the global Galois correspondence realized on the cohomology of the same Shimura varieties. The local Langlands conjecture is obtained as a corollary. Certain techniques developed in this book should extend to more general Shimura varieties, providing new instances of the local Langlands conjecture. Moreover, the geometry of the special fibers is strictly analogous to that of Shimura curves and can be expected to have applications to a variety of questions in number theory.
Book Synopsis An Introduction to the Langlands Program by : Joseph Bernstein
Download or read book An Introduction to the Langlands Program written by Joseph Bernstein and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a broad, user-friendly introduction to the Langlands program, that is, the theory of automorphic forms and its connection with the theory of L-functions and other fields of mathematics. Each of the twelve chapters focuses on a particular topic devoted to special cases of the program. The book is suitable for graduate students and researchers.
Book Synopsis Vision Geometry by : Robert A. Melter
Download or read book Vision Geometry written by Robert A. Melter and published by American Mathematical Soc.. This book was released on 1991 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its genesis more than thirty-five years ago, the field of computer vision has been known by various names, including pattern recognitions, image analysis, and image understanding. The central problem of computer vision is obtaining descriptive information by computer analysis of images of a scene. Together with the related fields of image processing and computer graphics, it has become an established discipline at the interface between computer science and electrical engineering. This volume contains fourteen papers presented at the AMS Special Session on Geometry Related to Computer Vision, held in Hoboken, New Jersey in Ooctober 1989. This book makes the results presented at the Special Session, which previously had been available only in the computer science literature, more widely available within the mathematical sciences community. Geometry plays a major role in computer vision since scene descriptions always involve geometrical properties of, and relations among, the objects of surfaces in the scene. The papers in this book provide a good sampling of geometric problems connected with computer vision. They deal with digital lines and curves, polygons, shape decompositions, digital connectedness and surfaces, digital metrics, and generalizations to higher-dimensional and graph-structured "spaces". Aimed at computer scientists specializing in image processing, computer vision, and pattern recognition - as well as mathematicians interested in applications to computer science - this book will provide readers with a view of how geometry is currently being applied to problems in computer vision.
Book Synopsis Spinor Construction of Vertex Operator Algebras, Triality, and $E^{(1)}_8$ by : Alex J. Feingold
Download or read book Spinor Construction of Vertex Operator Algebras, Triality, and $E^{(1)}_8$ written by Alex J. Feingold and published by American Mathematical Soc.. This book was released on 1991 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of vertex operator algebras is a remarkably rich new mathematical field which captures the algebraic content of conformal field theory in physics. Ideas leading up to this theory appeared in physics as part of statistical mechanics and string theory. In mathematics, the axiomatic definitions crystallized in the work of Borcherds and in Vertex Operator Algebras and the Monster, by Frenkel, Lepowsky, and Meurman. The structure of monodromies of intertwining operators for modules of vertex operator algebras yield braid group representations and leads to natural generalizations of vertex operator algebras, such as superalgebras and para-algebras. Many examples of vertex operator algebras and their generalizations are related to constructions in classical representation theory and shed new light on the classical theory. This book accomplishes several goals. The authors provide an explicit spinor construction, using only Clifford algebras, of a vertex operator superalgebra structure on the direct sum of the basic and vector modules for the affine Kac-Moody algebra Dn(1). They also review and extend Chevalley's spinor construction of the 24-dimensional commutative nonassociative algebraic structure and triality on the direct sum of the three 8-dimensional D4-modules. Vertex operator para-algebras, introduced and developed independently in this book and by Dong and Lepowsky, are related to one-dimensional representations of the braid group. The authors also provide a unified approach to the Chevalley, Greiss, and E8 algebras and explain some of their similarities. A Third goal is to provide a purely spinor construction of the exceptional affine Lie algebra E8(1), a natural continuation of previous work on spinor and oscillator constructions of the classical affine Lie algebras. These constructions should easily extend to include the rest of the exceptional affine Lie algebras. The final objective is to develop an inductive technique of construction which could be applied to the Monster vertex operator algebra. Directed at mathematicians and physicists, this book should be accessible to graduate students with some background in finite-dimensional Lie algebras and their representations. Although some experience with affine Kac-Moody algebras would be useful, a summary of the relevant parts of that theory is included. This book shows how the concepts and techniques of Lie theory can be generalized to yield the algebraic structures associated with conformal field theory. The careful reader will also gain a detailed knowledge of how the spinor construction of classical triality lifts to the affine algebras and plays an important role in the spinor construction of vertex operator algebras, modules, and intertwining operators with nontrivial monodromies.
Book Synopsis Integral Geometry and Tomography by : Eric Grinberg
Download or read book Integral Geometry and Tomography written by Eric Grinberg and published by American Mathematical Soc.. This book was released on 1990 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Integral Geometry and Tomography, held in June 1989 at Humboldt State University in Arcata, California. This book features articles that range over such diverse areas as combinatorics, geometric inequalities, micro-local analysis, group theory, and harmonic analysis.
Book Synopsis Algebraic Geometry: Sundance 1988 by : Brian Harbourne
Download or read book Algebraic Geometry: Sundance 1988 written by Brian Harbourne and published by American Mathematical Soc.. This book was released on 1991 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the NSF-CBMS Regional Conference on Algebraic Geometry, held in Sundance, Utah in July 1988. The conference focused on algebraic curves and related varieties. Some of the papers collected here represent lectures delivered at the conference, some report on research done during the conference, while others describe related work carried out elsewhere.
Book Synopsis Logic and Computation by : Wilfried Sieg
Download or read book Logic and Computation written by Wilfried Sieg and published by American Mathematical Soc.. This book was released on 1990 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Workshop on Logic and Computation, held in July 1987 at Carnegie-Mellon University. The focus of the workshop was the refined interaction between mathematics and computation theory, one of the most fascinating and potentially fruitful developments in logic. The importance of this interaction lies not only in the emergence of the computer as a powerful tool in mathematics research, but also in the various attempts to carry out significant parts of mathematics in computationally informative ways. The proceedings pursue three complementary aims: to develop parts of mathematics under minimal set-theoretic assumptions; to provide formal frameworks suitable for computer implementation; and to extract, from formal proofs, mathematical and computational information. Aimed at logicians, mathematicians, and computer scientists, this volume is rich in results and replete with mathematical, logical, and computational problems.
Book Synopsis Lie Algebras and Related Topics by : Georgia Benkart
Download or read book Lie Algebras and Related Topics written by Georgia Benkart and published by American Mathematical Soc.. This book was released on 1990 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses the problem of determining the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic $p>7$. This book includes topics such as Lie algebras of prime characteristic, algebraic groups, combinatorics and representation theory, and Kac-Moody and Virasoro algebras.
Book Synopsis Recent Developments in Geometry by : Robert Everist Greene
Download or read book Recent Developments in Geometry written by Robert Everist Greene and published by American Mathematical Soc.. This book was released on 1989 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the outgrowth of a Special Session on Geometry, held at the November 1987 meeting of the AMS at the University of California at Los Angeles. The unusually well-attended session attracted more than sixty participants and featured over forty addresses by some of the day's outstanding geometers. By common consent, it was decided that the papers to be collected in the present volume should be surveys of relatively broad areas of geometry, rather than detailed presentations of new research results. A comprehensive survey of the field is beyond the scope of a volume such as this. Nonetheless, the editors have sought to provide all geometers, whatever their specialties, with some insight into recent developments in a variety of topics in this active area of research.
Book Synopsis Current Progress in Hyperbolic Systems: Riemann Problems and Computations by : W. Brent Lindquist
Download or read book Current Progress in Hyperbolic Systems: Riemann Problems and Computations written by W. Brent Lindquist and published by American Mathematical Soc.. This book was released on 1989 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Current Progress in Hyperbolic Systems: Riemann Problems and Computations, held at Bowdoin College in July 1988.
Book Synopsis Proceedings of the International Conference on Algebra Dedicated to the Memory of A. I. Mal$'$cev by : Leonid A. Bokut'
Download or read book Proceedings of the International Conference on Algebra Dedicated to the Memory of A. I. Mal$'$cev written by Leonid A. Bokut' and published by American Mathematical Soc.. This book was released on 1992 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Abelian Groups and Noncommutative Rings: A Collection of Papers in Memory of Robert B. Warfield, Jr. by : László Fuchs
Download or read book Abelian Groups and Noncommutative Rings: A Collection of Papers in Memory of Robert B. Warfield, Jr. written by László Fuchs and published by American Mathematical Soc.. This book was released on 1992 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of research papers is dedicated to the memory of the distinguished algebraist Robert B. Warfield, Jr. Focusing on abelian group theory and noncommutative ring theory, the book covers a wide range of topics reflecting Warfield's interests and includes two articles surveying his contributions to mathematics. Because the articles have been refereed to high standards and will not appear elsewhere, this volume is indispensable to any researcher in noncommutative ring theory or abelian group theory. With papers by some of the major leaders in the field, this book will also be important to anyone interested in these areas, as it provides an overview of current research directions.
Book Synopsis Oscillation and Dynamics in Delay Equations by : John R. Graef
Download or read book Oscillation and Dynamics in Delay Equations written by John R. Graef and published by American Mathematical Soc.. This book was released on 1992 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Oscillation theory and dynamical systems have long been rich and active areas of research. Containing frontier contributions by some of the leaders in the field, this book brings together papers based on presentations at the AMS meeting in San Francisco in January 1991. With special emphasis on delay equations, the papers cover a broad range of topics in ordinary, partial, and difference equations and include applications to problems in commodity prices, biological modelling, and number theory. The book would be of interest to graduate students and researchers in mathematics or those in other fields who have an interest in delay equations and their applications.
Book Synopsis Invariant Theory by : Robert M. Fossum
Download or read book Invariant Theory written by Robert M. Fossum and published by American Mathematical Soc.. This book was released on 1989 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Invariant Theory, held in Denton, Texas in the fall of 1986; also included are several invited papers in this area. The purpose of the conference was to exchange ideas on recent developments in algebraic group actions on algebraic varieties. The papers fall into three main categories: actions of linear algebraic groups; flag manifolds and invariant theory; and representation theory and invariant theory. This book is likely to find a wide audience, for invariant theory is connected to a range of mathematical fields, such as algebraic groups, algebraic geometry, commutative algebra, and representation theory.
