Author: Edward FrenkelPublisher:
ISBN: 9780511294204
Category : Loops (Group theory)
Languages : en
Pages : 379
Book Description
Langlands Correspondence for Loop Groups
Author: Edward FrenkelPublisher:
ISBN: 9780511294204
Category : Loops (Group theory)
Languages : en
Pages : 379
Book Description
Langlands Correspondence for Loop Groups
Author: Edward FrenkelPublisher: Cambridge University Press
ISBN: 0521854431
Category : Mathematics
Languages : en
Pages : 5
Book Description
The first account of local geometric Langlands Correspondence, a new area of mathematical physics developed by the author.
Langlands Correspondence for Loop Groups ICM Edition
Author: Edward FrenkelPublisher:
ISBN: 9780521168892
Category :
Languages : en
Pages : 379
Book Description
Gerbal Representations of Double Loop Groups
Author: Xinwen ZhuRepresentation Theory and Complex Analysis
Author: Michael CowlingPublisher: Springer Science & Business Media
ISBN: 3540768912
Category : Mathematics
Languages : en
Pages : 400
Book Description
Six leading experts lecture on a wide spectrum of recent results on the subject of the title. They present a survey of various interactions between representation theory and harmonic analysis on semisimple groups and symmetric spaces, and recall the concept of amenability. They further illustrate how representation theory is related to quantum computing; and much more. Taken together, this volume provides both a solid reference and deep insights on current research activity.
Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry
Author: Sergey NovikovPublisher: American Mathematical Soc.
ISBN: 1470455927
Category : Education
Languages : en
Pages : 480
Book Description
This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.
Linear Algebraic Groups and Finite Groups of Lie Type
Author: Gunter MallePublisher: Cambridge University Press
ISBN: 113949953X
Category : Mathematics
Languages : en
Pages : 324
Book Description
Originating from a summer school taught by the authors, this concise treatment includes many of the main results in the area. An introductory chapter describes the fundamental results on linear algebraic groups, culminating in the classification of semisimple groups. The second chapter introduces more specialized topics in the subgroup structure of semisimple groups and describes the classification of the maximal subgroups of the simple algebraic groups. The authors then systematically develop the subgroup structure of finite groups of Lie type as a consequence of the structural results on algebraic groups. This approach will help students to understand the relationship between these two classes of groups. The book covers many topics that are central to the subject, but missing from existing textbooks. The authors provide numerous instructive exercises and examples for those who are learning the subject as well as more advanced topics for research students working in related areas.
Representations of Groups
Author: Klaus LuxPublisher: Cambridge University Press
ISBN: 1139489186
Category : Mathematics
Languages : en
Pages : 471
Book Description
The representation theory of finite groups has seen rapid growth in recent years with the development of efficient algorithms and computer algebra systems. This is the first book to provide an introduction to the ordinary and modular representation theory of finite groups with special emphasis on the computational aspects of the subject. Evolving from courses taught at Aachen University, this well-paced text is ideal for graduate-level study. The authors provide over 200 exercises, both theoretical and computational, and include worked examples using the computer algebra system GAP. These make the abstract theory tangible and engage students in real hands-on work. GAP is freely available from www.gap-system.org and readers can download source code and solutions to selected exercises from the book's web page.
Integral Geometry Methods in the Geometrical Langlands Program
Author: Prof. Dr. Francisco BulnesPublisher: Scientific Research Publishing, Inc. USA
ISBN: 1618961403
Category : Mathematics
Languages : en
Pages : 195
Book Description
The book is divided on the studied aspects in integral geometry and that are of interest in field theory, at least, to the solution or obtaining of integrals to the field equations corresponding to the moduli stacks planted. In the chapters 1, 2, 3, 4, are exposed the generalizations of the Penrose transforms with a good D-modules theory in the derived categories context and their deformations. In the chapters 5, and 6, are exposed and discussed the different classification problems and their implications in the differential operators to the field equations. Finally, in the chapters 7, and 8 are exposed the aspects of the geometrical ramification of field ramification going behold the holomorphicity. In the end of the book are included several research exercises that can be discussed and exposed inside postgraduate courses in derived geometry or related as derived categories or categories on commutative and non-commutative rings.
Galois Groups and Fundamental Groups
Author: Tamás SzamuelyPublisher: Cambridge University Press
ISBN: 1139481142
Category : Mathematics
Languages : en
Pages : 281
Book Description
Ever since the concepts of Galois groups in algebra and fundamental groups in topology emerged during the nineteenth century, mathematicians have known of the strong analogies between the two concepts. This book presents the connection starting at an elementary level, showing how the judicious use of algebraic geometry gives access to the powerful interplay between algebra and topology that underpins much modern research in geometry and number theory. Assuming as little technical background as possible, the book starts with basic algebraic and topological concepts, but already presented from the modern viewpoint advocated by Grothendieck. This enables a systematic yet accessible development of the theories of fundamental groups of algebraic curves, fundamental groups of schemes, and Tannakian fundamental groups. The connection between fundamental groups and linear differential equations is also developed at increasing levels of generality. Key applications and recent results, for example on the inverse Galois problem, are given throughout.