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Representations of SL2 Fq

Representations of SL2 Fq Author Cédric Bonnafé
ISBN-10 0857291572
Release 2010-10-08
Pages 186
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Deligne-Lusztig theory aims to study representations of finite reductive groups by means of geometric methods, and particularly l-adic cohomology. Many excellent texts present, with different goals and perspectives, this theory in the general setting. This book focuses on the smallest non-trivial example, namely the group SL2(Fq), which not only provides the simplicity required for a complete description of the theory, but also the richness needed for illustrating the most delicate aspects. The development of Deligne-Lusztig theory was inspired by Drinfeld's example in 1974, and Representations of SL2(Fq) is based upon this example, and extends it to modular representation theory. To this end, the author makes use of fundamental results of l-adic cohomology. In order to efficiently use this machinery, a precise study of the geometric properties of the action of SL2(Fq) on the Drinfeld curve is conducted, with particular attention to the construction of quotients by various finite groups. At the end of the text, a succinct overview (without proof) of Deligne-Lusztig theory is given, as well as links to examples demonstrated in the text. With the provision of both a gentle introduction and several recent materials (for instance, Rouquier's theorem on derived equivalences of geometric nature), this book will be of use to graduate and postgraduate students, as well as researchers and lecturers with an interest in Deligne-Lusztig theory.

Basic Structures of Function Field Arithmetic

Basic Structures of Function Field Arithmetic Author David Goss
ISBN-10 9783642614804
Release 2012-12-06
Pages 424
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From the reviews:"The a thorough and very readable introduction to the arithmetic of function fields of one variable over a finite field, by an author who has made fundamental contributions to the field. It serves as a definitive reference volume, as well as offering graduate students with a solid understanding of algebraic number theory the opportunity to quickly reach the frontiers of knowledge in an important area of mathematics...The arithmetic of function fields is a universe filled with beautiful surprises, in which familiar objects from classical number theory reappear in new guises, and in which entirely new objects play important roles. Goss'clear exposition and lively style make this book an excellent introduction to this fascinating field." MR 97i:11062

Magyarorsz g vi k nyv szete

Magyarorsz  g   vi k  nyv  szete Author
ISBN-10 STANFORD:36105117258967
Release 1987
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Magyarorsz g vi k nyv szete has been writing in one form or another for most of life. You can find so many inspiration from Magyarorsz g vi k nyv szete also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Magyarorsz g vi k nyv szete book for free.

Magyar nemzeti bibliogr fia

Magyar nemzeti bibliogr  fia Author
ISBN-10 UOM:39015036780800
Release 1986
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Magyar nemzeti bibliogr fia has been writing in one form or another for most of life. You can find so many inspiration from Magyar nemzeti bibliogr fia also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Magyar nemzeti bibliogr fia book for free.

The Large Sieve and its Applications

The Large Sieve and its Applications Author E. Kowalski
ISBN-10 9781139472975
Release 2008-05-22
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Among the modern methods used to study prime numbers, the 'sieve' has been one of the most efficient. Originally conceived by Linnik in 1941, the 'large sieve' has developed extensively since the 1960s, with a recent realisation that the underlying principles were capable of applications going well beyond prime number theory. This book develops a general form of sieve inequality, and describes its varied applications, including the study of families of zeta functions of algebraic curves over finite fields; arithmetic properties of characteristic polynomials of random unimodular matrices; homological properties of random 3-manifolds; and the average number of primes dividing the denominators of rational points on elliptic curves. Also covered in detail are the tools of harmonic analysis used to implement the forms of the large sieve inequality, including the Riemann Hypothesis over finite fields, and Property (T) or Property (tau) for discrete groups.

Introduction to Quantum Groups

Introduction to Quantum Groups Author George Lusztig
ISBN-10 0817647171
Release 2010-10-27
Pages 352
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The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical basis with rather remarkable properties. This book will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists and to theoretical physicists and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the book could also be used as a text book.

A Tale of Two Fractals

A Tale of Two Fractals Author A.A. Kirillov
ISBN-10 9780817683825
Release 2013-04-23
Pages 138
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Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. Despite the volume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use. Written by celebrated mathematician and educator A.A. Kirillov, A Tale of Two Fractals is intended to help bridge this gap, providing an original treatment of fractals that is at once accessible to beginners and sufficiently rigorous for serious mathematicians. The work is designed to give young, non-specialist mathematicians a solid foundation in the theory of fractals, and, in the process, to equip them with exposure to a variety of geometric, analytical, and algebraic tools with applications across other areas.

Discriminants Resultants and Multidimensional Determinants

Discriminants  Resultants  and Multidimensional Determinants Author Israel M. Gelfand
ISBN-10 9780817647711
Release 2009-05-21
Pages 523
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"This book revives and vastly expands the classical theory of resultants and discriminants. Most of the main new results of the book have been published earlier in more than a dozen joint papers of the authors. The book nicely complements these original papers with many examples illustrating both old and new results of the theory."—Mathematical Reviews

The Finite Simple Groups

The Finite Simple Groups Author Robert Wilson
ISBN-10 9781848009875
Release 2009-12-14
Pages 298
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Here, a thorough grounding in the theory of alternating and classical groups is followed by discussion of exceptional groups (classed as automorphism groups of multilinear forms), sporadic and Chevalley groups, as well as the theory of Lie algebras.

Representations of Finite Classical Groups

Representations of Finite Classical Groups Author A. V. Zelevinsky
ISBN-10 9783540387114
Release 2006-11-14
Pages 186
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Representations of Finite Classical Groups has been writing in one form or another for most of life. You can find so many inspiration from Representations of Finite Classical Groups also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Representations of Finite Classical Groups book for free.

Linear Representations of Finite Groups

Linear Representations of Finite Groups Author Jean-Pierre Serre
ISBN-10 9781468494587
Release 2012-12-06
Pages 172
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This book consists of three parts, rather different in level and purpose. The first part was originally written for quantum chemists. It describes the correspondence, due to Frobenius, between linear representations and characters. The second part is a course given in 1966 to second-year students of l’Ecole Normale. It completes in a certain sense the first part. The third part is an introduction to Brauer Theory.

Simple Groups of Lie Type

Simple Groups of Lie Type Author Roger W. Carter
ISBN-10 0471506834
Release 1989-01-18
Pages 364
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Now available in paperback--the standard introduction to the theory of simple groups of Lie type. In 1955, Chevalley showed how to construct analogues of the complex simple Lie groups over arbitrary fields. The present work presents the basic results in the structure theory of Chevalley groups and their twisted analogues. Carter looks at groups of automorphisms of Lie algebras, makes good use of Weyl group (also discussing Lie groups over finite fields), and develops the theory of Chevalley and Steinberg groups in the general context of groups with a (B,N)-pair. This new edition contains a corrected proof of the simplicity of twisted groups, a completed list of sporadic simple groups in the final chapter and a few smaller amendments; otherwise, this work remains the classic piece of exposition it was when it first appeared in 1971.

Theorems and Problems in Functional Analysis

Theorems and Problems in Functional Analysis Author A. A. Kirillov
ISBN-10 9781461381532
Release 2012-12-06
Pages 347
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Even the simplest mathematical abstraction of the phenomena of reality the real line-can be regarded from different points of view by different mathematical disciplines. For example, the algebraic approach to the study of the real line involves describing its properties as a set to whose elements we can apply" operations," and obtaining an algebraic model of it on the basis of these properties, without regard for the topological properties. On the other hand, we can focus on the topology of the real line and construct a formal model of it by singling out its" continuity" as a basis for the model. Analysis regards the line, and the functions on it, in the unity of the whole system of their algebraic and topological properties, with the fundamental deductions about them obtained by using the interplay between the algebraic and topological structures. The same picture is observed at higher stages of abstraction. Algebra studies linear spaces, groups, rings, modules, and so on. Topology studies structures of a different kind on arbitrary sets, structures that give mathe matical meaning to the concepts of a limit, continuity, a neighborhood, and so on. Functional analysis takes up topological linear spaces, topological groups, normed rings, modules of representations of topological groups in topological linear spaces, and so on. Thus, the basic object of study in functional analysis consists of objects equipped with compatible algebraic and topological structures.

Lectures on the Orbit Method

Lectures on the Orbit Method Author Aleksandr Aleksandrovich Kirillov
ISBN-10 9780821835302
Release 2004
Pages 408
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Isaac Newton encrypted his discoveries in analysis in the form of an anagram that deciphers to the sentence, 'It is worthwhile to solve differential equations'. Accordingly, one can express the main idea behind the orbit method by saying 'It is worthwhile to study coadjoint orbits'. The orbit method was introduced by the author, A. A. Kirillov, in the 1960s and remains a useful and powerful tool in areas such as Lie theory, group representations, integrable systems, complex and symplectic geometry, and mathematical physics. This book describes the essence of the orbit method for non-experts and gives the first systematic, detailed, and self-contained exposition of the method. It starts with a convenient 'User's Guide' and contains numerous examples. It can be used as a text for a graduate course, as well as a handbook for non-experts and a reference book for research mathematicians and mathematical physicists.

Harmonic Analysis on Symmetric Spaces Euclidean Space the Sphere and the Poincar Upper Half Plane

Harmonic Analysis on Symmetric Spaces   Euclidean Space  the Sphere  and the Poincar   Upper Half Plane Author Audrey Terras
ISBN-10 9781461479727
Release 2013-09-12
Pages 413
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This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincaré upper half plane. This book is intended for beginning graduate students in mathematics or researchers in physics or engineering. Written with an informal style, the book places an emphasis on motivation, concrete examples, history, and, above all, applications in mathematics, statistics, physics, and engineering. Many corrections and updates have been incorporated in this new edition. Updates include discussions of P. Sarnak and others' work on quantum chaos, the work of T. Sunada, Marie-France Vignéras, Carolyn Gordon, and others on Mark Kac's question "Can you hear the shape of a drum?", A. Lubotzky, R. Phillips and P. Sarnak's examples of Ramanujan graphs, and, finally, the author's comparisons of continuous theory with the finite analogues. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, Poisson's summation formula and applications in crystallography and number theory, applications of spherical harmonic analysis to the hydrogen atom, the Radon transform, non-Euclidean geometry on the Poincaré upper half plane H or unit disc and applications to microwave engineering, fundamental domains in H for discrete groups Γ, tessellations of H from such discrete group actions, automorphic forms, and the Selberg trace formula and its applications in spectral theory as well as number theory.

Representation Theory and Noncommutative Harmonic Analysis I

Representation Theory and Noncommutative Harmonic Analysis I Author Alexandre Kirillov
ISBN-10 3540186980
Release 1994-11-23
Pages 236
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This two-part survey provides a short review of the classical part of representation theory, carefully exposing the structure of the theory without overwhelming readers with details, and deals with representations of Virasoro and Kac-Moody algebra. It presents a wealth of recent results on representations of infinite-dimensional groups.

Nonconservative Stability Problems of Modern Physics

Nonconservative Stability Problems of Modern Physics Author Oleg N. Kirillov
ISBN-10 9783110270433
Release 2013-06-26
Pages 446
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This work gives a complete overview on the subject of nonconservative stability from the modern point of view. Relevant mathematical concepts are presented, as well as rigorous stability results and numerous classical and contemporary examples from mechanics and physics. The book shall serve to present and prospective specialists providing the current state of knowledge in this actively developing field. The understanding of this theory is vital for many areas of technology, as dissipative effects in rotor dynamics or celestial mechanics.