Notes On Coxeter Transformations And The Mckay Correspondence

Author : Rafael Stekolshchik
Publisher : Springer Science & Business Media
Page : 250 pages
File Size : 43,6 Mb
Release : 2008-01-18
Category : Mathematics
ISBN : 9783540773993

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Notes on Coxeter Transformations and the McKay Correspondence by Rafael Stekolshchik Pdf

Here is a key text on the subject of representation theory in finite groups. The pages of this excellent little book, prepared by Rafael Stekolshchik, contain a number of new proofs relating to Coxeter Transformations and the McKay Correspondence. They include ideas and formulae from a number of luminaries including J. N. Bernstein, I. M. Gelfand and V. A. Ponomarev, as well as material from Coxeter and McKay themselves. Many other authors have material published here too.

Author : Gustav I. Lehrer,Donald E. Taylor
Publisher : Cambridge University Press
Page : 303 pages
File Size : 46,9 Mb
Release : 2009-08-13
Category : Mathematics
ISBN : 9780521749893

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Unitary Reflection Groups by Gustav I. Lehrer,Donald E. Taylor Pdf

A unitary reflection is a linear transformation of a complex vector space that fixes each point in a hyperplane. Intuitively, it resembles the transformation an image undergoes when it is viewed through a kaleidoscope, or an arrangement of mirrors. This book gives a complete classification of all finite groups which are generated by unitary reflections, using the method of line systems. Irreducible groups are studied in detail, and are identified with finite linear groups. The new invariant theoretic proof of Steinberg's fixed point theorem is treated fully. The same approach is used to develop the theory of eigenspaces of elements of reflection groups and their twisted analogues. This includes an extension of Springer's theory of regular elements to reflection cosets. An appendix outlines links to representation theory, topology and mathematical physics. Containing over 100 exercises, ranging in difficulty from elementary to research level, this book is ideal for honours and graduate students, or for researchers in algebra, topology and mathematical physics. Book jacket.

Author : Michiel Hazewinkel,Nadezhda Mikhaĭlovna Gubareni,Vladimir V. Kirichenko
Publisher : American Mathematical Soc.
Page : 425 pages
File Size : 44,9 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821852620

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Algebras, Rings and Modules by Michiel Hazewinkel,Nadezhda Mikhaĭlovna Gubareni,Vladimir V. Kirichenko Pdf

Presenting an introduction to the theory of Hopf algebras, the authors also discuss some important aspects of the theory of Lie algebras. This book includes a chapters on the Hopf algebra of symmetric functions, the Hopf algebra of representations of the symmetric groups, the Hopf algebras of the nonsymmetric and quasisymmetric functions, and the Hopf algebra of permutations.

Author : Arkadiusz Jadczyk
Publisher : World Scientific
Page : 360 pages
File Size : 53,7 Mb
Release : 2014-07-23
Category : Science
ISBN : 9789814569880

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Quantum Fractals by Arkadiusz Jadczyk Pdf

Starting with numerical algorithms resulting in new kinds of amazing fractal patterns on the sphere, this book describes the theory underlying these phenomena and indicates possible future applications. The book also explores the following questions: What are fractals?How do fractal patterns emerge from quantum observations and relativistic light aberration effects?What are the open problems with iterated function systems based on Mobius transformations?Can quantum fractals be experimentally detected?What are quantum jumps?Is quantum theory complete and/or universal?Is the standard interpretation of Heisenberg's uncertainty relations accurate?What is Event Enhanced Quantum Theory and how does it differ from spontaneous localization theories?What are the possible applications of quantum fractals? Contents:IntroductionWhat are Quantum Fractals?:Cantor SetIterated Function SystemsCantor Set Through Matrix EigenvectorQuantum Iterated Function SystemsExample: The "Impossible" Quantum FractalAction on the PlaneLorentz Group, SL(2,ℂ), and Relativistic AberrationExamples:Hyperbolic Quantum FractalsControlling Chaotic Behavior and Fractal DimensionQuantum Fractals on n-SpheresAlgorithms for Generating Hyperbolic Quantum FractalsFoundational Questions:Stochastic Nature of Quantum Measurement ProcessesAre There Quantum Jumps?Bohmian MechanicsEvent Enhanced Quantum TheoryGhirardi–Rimini–Weber Spontaneous LocalizationHeisenberg's Uncertainty Principle and Quantum FractalsAre Quantum Fractals Real?Appendix A. Mathematical Concepts:Metric SpacesNormed SpacesMeasure and IntegralMarkov, Frobenius-Perron and Koopman OperatorsAppendix B. Minkowski Space Generalization of Euler-Rodrigues Formula:Alternative Derivation via SL(2,ℂ) Readership: Advanced undergraduate students and professionals in quantum chaos, as well as philosophers of science. Keywords:Fractals;Quantum Theory;Measurement;Uncertainty;Quantum Jumps;Mobius Transformations;IFS;Spin;Lorentz Group;Relativity;Aberration;Time;GRW;EEQT

Author : George Grätzer,Friedrich Wehrung
Publisher : Birkhäuser
Page : 616 pages
File Size : 41,7 Mb
Release : 2016-10-08
Category : Mathematics
ISBN : 9783319442365

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Lattice Theory: Special Topics and Applications by George Grätzer,Friedrich Wehrung Pdf

George Grätzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Grätzer considered updating the second edition to reflect some exciting and deep developments. He soon realized that to lay the foundation, to survey the contemporary field, to pose research problems, would require more than one volume and more than one person. So Lattice Theory: Foundation provided the foundation. Now we complete this project with Lattice Theory: Special Topics and Applications, in two volumes, written by a distinguished group of experts, to cover some of the vast areas not in Foundation. This second volume is divided into ten chapters contributed by K. Adaricheva, N. Caspard, R. Freese, P. Jipsen, J.B. Nation, N. Reading, H. Rose, L. Santocanale, and F. Wehrung.

Author : Die deutsche Nationalbibliothek
Publisher : Unknown
Page : 830 pages
File Size : 54,8 Mb
Release : 2008
Category : Electronic
ISBN : 16136438

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Deutsche Nationalbibliografie by Die deutsche Nationalbibliothek Pdf

Author : American Mathematical Society
Publisher : American Mathematical Soc.
Page : 258 pages
File Size : 44,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821848814

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Selected Papers on Analysis and Differential Equations by American Mathematical Society Pdf

"Volume includes English translation of ten expository articles published in the Japanese journal Sugaku."

Author : Ola Bratteli,Sergey Neshveyev,Christian Skau
Publisher : Springer Science & Business Media
Page : 280 pages
File Size : 52,9 Mb
Release : 2007-01-19
Category : Mathematics
ISBN : 9783540341970

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Operator Algebras by Ola Bratteli,Sergey Neshveyev,Christian Skau Pdf

The theme of the first Abel Symposium was operator algebras in a wide sense. In the last 40 years operator algebras have developed from a rather special discipline within functional analysis to become a central field in mathematics often described as "non-commutative geometry". It has branched out in several sub-disciplines and made contact with other subjects. The contributions to this volume give a state-of-the-art account of some of these sub-disciplines and the variety of topics reflect to some extent how the subject has developed. This is the first volume in a prestigious new book series linked to the Abel prize.

Author : Kazuhiro Konno,Viet Nguyen-Khac
Publisher : Unknown
Page : 366 pages
File Size : 41,8 Mb
Release : 2008
Category : Mathematics
ISBN : UOM:39015075621295

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Algebraic Geometry in East Asia by Kazuhiro Konno,Viet Nguyen-Khac Pdf

This volume contains two survey articles and eight research articles contributed by the invited lecturers at the conference Algebraic Geometry in East Asia. II, which was held at the Conference Hall (Hanoi, Vietnam) from October 10-14, 2005. Topics touched upon in this volume include Zariski pairs, rational homogeneous manifolds, Kummer surfaces, singularity theory, Cremona groups, algebraic curves, dual varieties, Castelnuovo-Weil lattices, etc. The reader can not only find the current status of a variety of research topics but also enjoy the art of the subjects presented by leading algebraic geometers.

Author : Terence Tao
Publisher : American Mathematical Soc.
Page : 303 pages
File Size : 48,8 Mb
Release : 2015-04-16
Category : Mathematics
ISBN : 9781470421960

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Expansion in Finite Simple Groups of Lie Type by Terence Tao Pdf

Expander graphs are an important tool in theoretical computer science, geometric group theory, probability, and number theory. Furthermore, the techniques used to rigorously establish the expansion property of a graph draw from such diverse areas of mathematics as representation theory, algebraic geometry, and arithmetic combinatorics. This text focuses on the latter topic in the important case of Cayley graphs on finite groups of Lie type, developing tools such as Kazhdan's property (T), quasirandomness, product estimates, escape from subvarieties, and the Balog-Szemerédi-Gowers lemma. Applications to the affine sieve of Bourgain, Gamburd, and Sarnak are also given. The material is largely self-contained, with additional sections on the general theory of expanders, spectral theory, Lie theory, and the Lang-Weil bound, as well as numerous exercises and other optional material.

Author : Clay Mathematics Institute. Summer School,Isaac Newton Institute for Mathematical Sciences
Publisher : American Mathematical Soc.
Page : 396 pages
File Size : 44,5 Mb
Release : 2004
Category : Mathematics
ISBN : 082183715X

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Strings and Geometry by Clay Mathematics Institute. Summer School,Isaac Newton Institute for Mathematical Sciences Pdf

Contains selection of expository and research article by lecturers at the school. Highlights current interests of researchers working at the interface between string theory and algebraic supergravity, supersymmetry, D-branes, the McKay correspondence andFourer-Mukai transform.

Author : Pavel I. Etingof
Publisher : European Mathematical Society
Page : 108 pages
File Size : 46,9 Mb
Release : 2007
Category : Mathematics
ISBN : 3037190345

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Calogero-Moser Systems and Representation Theory by Pavel I. Etingof Pdf

Calogero-Moser systems, which were originally discovered by specialists in integrable systems, are currently at the crossroads of many areas of mathematics and within the scope of interests of many mathematicians. More specifically, these systems and their generalizations turned out to have intrinsic connections with such fields as algebraic geometry (Hilbert schemes of surfaces), representation theory (double affine Hecke algebras, Lie groups, quantum groups), deformation theory (symplectic reflection algebras), homological algebra (Koszul algebras), Poisson geometry, etc. The goal of the present lecture notes is to give an introduction to the theory of Calogero-Moser systems, highlighting their interplay with these fields. Since these lectures are designed for non-experts, the author gives short introductions to each of the subjects involved and provides a number of exercises.

Author : P. Slodowy
Publisher : Springer
Page : 187 pages
File Size : 53,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540381914

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Simple Singularities and Simple Algebraic Groups by P. Slodowy Pdf

Author : James E. Humphreys
Publisher : Cambridge University Press
Page : 222 pages
File Size : 52,9 Mb
Release : 1992-10
Category : Mathematics
ISBN : 0521436133

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Reflection Groups and Coxeter Groups by James E. Humphreys Pdf

This graduate textbook presents a concrete and up-to-date introduction to the theory of Coxeter groups. The book is self-contained, making it suitable either for courses and seminars or for self-study. The first part is devoted to establishing concrete examples. Finite reflection groups acting on Euclidean spaces are discussed, and the first part ends with the construction of the affine Weyl groups, a class of Coxeter groups that plays a major role in Lie theory. The second part (which is logically independent of, but motivated by, the first) develops from scratch the properties of Coxeter groups in general, including the Bruhat ordering and the seminal work of Kazhdan and Lusztig on representations of Hecke algebras associated with Coxeter groups is introduced. Finally a number of interesting complementary topics as well as connections with Lie theory are sketched. The book concludes with an extensive bibliography on Coxeter groups and their applications.

Author : Pavel I. Etingof,Oleg Golberg,Sebastian Hensel ,Tiankai Liu ,Alex Schwendner ,Dmitry Vaintrob ,Elena Yudovina
Publisher : American Mathematical Soc.
Page : 240 pages
File Size : 51,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821853511

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Introduction to Representation Theory by Pavel I. Etingof,Oleg Golberg,Sebastian Hensel ,Tiankai Liu ,Alex Schwendner ,Dmitry Vaintrob ,Elena Yudovina Pdf

Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.