Read Books Online and Download eBooks, EPub, PDF, Mobi, Kindle, Text Full Free.
Reflection Groups And Coxeter Groups
Download Reflection Groups And Coxeter Groups full books in PDF, epub, and Kindle. Read online Reflection Groups And Coxeter Groups ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Book Synopsis Reflection Groups and Coxeter Groups by : James E. Humphreys
Download or read book Reflection Groups and Coxeter Groups written by James E. Humphreys and published by Cambridge University Press. This book was released on 1992-10 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Geometry and Topology of Coxeter Groups by : Michael Davis
Download or read book The Geometry and Topology of Coxeter Groups written by Michael Davis and published by Princeton University Press. This book was released on 2008 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book. The book explains a theorem of Moussong that demonstrates that a polyhedral metric on this cell complex is nonpositively curved, meaning that Coxeter groups are "CAT(0) groups." The book describes the reflection group trick, one of the most potent sources of examples of aspherical manifolds. And the book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincaré Conjecture; and Gromov's theory of CAT(0) spaces and groups. Finally, the book examines connections between Coxeter groups and some of topology's most famous open problems concerning aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer conjectures.
Book Synopsis Reflection Groups and Invariant Theory by : Richard Kane
Download or read book Reflection Groups and Invariant Theory written by Richard Kane and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reflection groups and invariant theory is a branch of mathematics that lies at the intersection between geometry and algebra. The book contains a deep and elegant theory, evolved from various graduate courses given by the author over the past 10 years.
Book Synopsis Finite Reflection Groups by : L.C. Grove
Download or read book Finite Reflection Groups written by L.C. Grove and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chapter 1 introduces some of the terminology and notation used later and indicates prerequisites. Chapter 2 gives a reasonably thorough account of all finite subgroups of the orthogonal groups in two and three dimensions. The presentation is somewhat less formal than in succeeding chapters. For instance, the existence of the icosahedron is accepted as an empirical fact, and no formal proof of existence is included. Throughout most of Chapter 2 we do not distinguish between groups that are "geo metrically indistinguishable," that is, conjugate in the orthogonal group. Very little of the material in Chapter 2 is actually required for the sub sequent chapters, but it serves two important purposes: It aids in the development of geometrical insight, and it serves as a source of illustrative examples. There is a discussion offundamental regions in Chapter 3. Chapter 4 provides a correspondence between fundamental reflections and funda mental regions via a discussion of root systems. The actual classification and construction of finite reflection groups takes place in Chapter 5. where we have in part followed the methods of E. Witt and B. L. van der Waerden. Generators and relations for finite reflection groups are discussed in Chapter 6. There are historical remarks and suggestions for further reading in a Post lude.
Book Synopsis Mirrors and Reflections by : Alexandre V. Borovik
Download or read book Mirrors and Reflections written by Alexandre V. Borovik and published by Springer Science & Business Media. This book was released on 2009-11-07 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate/advanced undergraduate textbook contains a systematic and elementary treatment of finite groups generated by reflections. The approach is based on fundamental geometric considerations in Coxeter complexes, and emphasizes the intuitive geometric aspects of the theory of reflection groups. Key features include: many important concepts in the proofs are illustrated in simple drawings, which give easy access to the theory; a large number of exercises at various levels of difficulty; some Euclidean geometry is included along with the theory of convex polyhedra; no prerequisites are necessary beyond the basic concepts of linear algebra and group theory; and a good index and bibliography The exposition is directed at advanced undergraduates and first-year graduate students.
Book Synopsis Combinatorics of Coxeter Groups by : Anders Bjorner
Download or read book Combinatorics of Coxeter Groups written by Anders Bjorner and published by Springer Science & Business Media. This book was released on 2006-02-25 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes a rich variety of exercises to accompany the exposition of Coxeter groups Coxeter groups have already been exposited from algebraic and geometric perspectives, but this book will be presenting the combinatorial aspects of Coxeter groups
Book Synopsis Coxeter Matroids by : Alexandre V. Borovik
Download or read book Coxeter Matroids written by Alexandre V. Borovik and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matroids appear in diverse areas of mathematics, from combinatorics to algebraic topology and geometry, and "Coxeter Matroids" provides an intuitive and interdisciplinary treatment of their theory. In this text, matroids are examined in terms of symmetric and finite reflection groups; also, symplectic matroids and the more general coxeter matroids are carefully developed. The Gelfand-Serganova theorem, which allows for the geometric interpretation of matroids as convex polytopes with certain symmetry properties, is presented, and in the final chapter, matroid representations and combinatorial flag varieties are discussed. With its excellent bibliography and index and ample references to current research, this work will be useful for graduate students and research mathematicians.
Book Synopsis Introduction to Soergel Bimodules by : Ben Elias
Download or read book Introduction to Soergel Bimodules written by Ben Elias and published by Springer Nature. This book was released on 2020-09-26 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to Soergel bimodules. First introduced by Wolfgang Soergel in the early 1990s, they have since become a powerful tool in geometric representation theory. On the one hand, these bimodules are fairly elementary objects and explicit calculations are possible. On the other, they have deep connections to Lie theory and geometry. Taking these two aspects together, they offer a wonderful primer on geometric representation theory. In this book the reader is introduced to the theory through a series of lectures, which range from the basics, all the way to the latest frontiers of research. This book serves both as an introduction and as a reference guide to the theory of Soergel bimodules. Thus it is intended for anyone who wants to learn about this exciting field, from graduate students to experienced researchers.
Book Synopsis Unitary Reflection Groups by : Gustav I. Lehrer
Download or read book Unitary Reflection Groups written by Gustav I. Lehrer and published by Cambridge University Press. This book was released on 2009-08-13 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Buildings and Classical Groups by : Paul B. Garrett
Download or read book Buildings and Classical Groups written by Paul B. Garrett and published by CRC Press. This book was released on 1997-04-01 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Buildings are highly structured, geometric objects, primarily used in the finer study of the groups that act upon them. In Buildings and Classical Groups, the author develops the basic theory of buildings and BN-pairs, with a focus on the results needed to apply it to the representation theory of p-adic groups. In particular, he addresses spherical and affine buildings, and the "spherical building at infinity" attached to an affine building. He also covers in detail many otherwise apocryphal results. Classical matrix groups play a prominent role in this study, not only as vehicles to illustrate general results but as primary objects of interest. The author introduces and completely develops terminology and results relevant to classical groups. He also emphasizes the importance of the reflection, or Coxeter groups and develops from scratch everything about reflection groups needed for this study of buildings. In addressing the more elementary spherical constructions, the background pertaining to classical groups includes basic results about quadratic forms, alternating forms, and hermitian forms on vector spaces, plus a description of parabolic subgroups as stabilizers of flags of subspaces. The text then moves on to a detailed study of the subtler, less commonly treated affine case, where the background concerns p-adic numbers, more general discrete valuation rings, and lattices in vector spaces over ultrametric fields. Buildings and Classical Groups provides essential background material for specialists in several fields, particularly mathematicians interested in automorphic forms, representation theory, p-adic groups, number theory, algebraic groups, and Lie theory. No other available source provides such a complete and detailed treatment.
Book Synopsis Reflection Groups and Invariant Theory by : Richard Kane
Download or read book Reflection Groups and Invariant Theory written by Richard Kane and published by Springer Science & Business Media. This book was released on 2001-06-21 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reflection groups and invariant theory is a branch of mathematics that lies at the intersection between geometry and algebra. The book contains a deep and elegant theory, evolved from various graduate courses given by the author over the past 10 years.
Author :Harold Scott Macdonald Coxeter Publisher :Springer Science & Business Media ISBN 13 :3662257394 Total Pages :163 pages Book Rating :4.6/5 (622 download)
Book Synopsis Generators and Relations for Discrete Groups by : Harold Scott Macdonald Coxeter
Download or read book Generators and Relations for Discrete Groups written by Harold Scott Macdonald Coxeter and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: When we began to consider the scope of this book, we envisaged a catalogue supplying at least one abstract definition for any finitely generated group that the reader might propose. But we soon realized that more or less arbitrary restrictions are necessary, because interesting groups are so numerous. For permutation groups of degree 8 or less (i. e., subgroups of e ), the reader cannot do better than consult the 8 tables of JosEPHINE BuRNS (1915), while keeping an eye open for misprints. Our own tables (on pages 134-143) deal with groups of low order, finiteandinfinite groups of congruent transformations, symmetric and alternating groups, linear fractional groups, and groups generated by reflections in real Euclidean space of any number of dimensions. The best substitute foramoreextensive catalogue is the description (in Chapter 2) of a method whereby the reader can easily work out his own abstract definition for almost any given finite group. This method is sufficiently mechanical for the use of an electronic computer. There is also a topological method (Chapter 3), suitable not only for groups of low order but also for some infinite groups. This involves choosing a set of generators, constructing a certain graph (the Cayley diagram or DEHNsehe Gruppenbild), and embedding the graph into a surface. Cases in which the surface is a sphere or a plane are described in Chapter 4, where we obtain algebraically, and verify topologically, an abstract definition for each of the 17 space groups of two-dimensional crystallography.
Book Synopsis Geometry of Coxeter Groups by : Howard Hiller
Download or read book Geometry of Coxeter Groups written by Howard Hiller and published by Pitman Publishing. This book was released on 1982 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Coxeter Groups and Hopf Algebras by : Marcelo Aguiar
Download or read book Coxeter Groups and Hopf Algebras written by Marcelo Aguiar and published by American Mathematical Soc.. This book was released on 2006 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: An important idea in the work of G.-C. Rota is that certain combinatorial objects give rise to Hopf algebras that reflect the manner in which these objects compose and decompose. Recent work has seen the emergence of several interesting Hopf algebras of this kind, which connect diverse subjects such as combinatorics, algebra, geometry, and theoretical physics. This monograph presents a novel geometric approach using Coxeter complexes and the projection maps of Tits for constructing and studying many of these objects as well as new ones. The first three chapters introduce the necessary background ideas making this work accessible to advanced graduate students. The later chapters culminate in a unified and conceptual construction of several Hopf algebras based on combinatorial objects which emerge naturally from the geometric viewpoint. This work lays a foundation and provides new insights for further development of the subject.
Book Synopsis Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras by : Meinolf Geck
Download or read book Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras written by Meinolf Geck and published by Oxford University Press. This book was released on 2000 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Coxeter groups and related structures arise naturally in several branches of mathematics such as the theory of Lie algebras and algebraic groups. The corresponding Iwahori-Hecke algebras are then obtained by a certain deformation process which have applications in the representation theory of groups of Lie type and the theory of knots and links. This book develops the theory of conjugacy classes and irreducible character, both for finite Coxeter groups and the associated Iwahori-Hecke algebras. Topics covered range from classical results to more recent developments and are clear and concise. This is the first book to develop these subjects both from a theoretical and an algorithmic point of view in a systematic way, covering all types of finite Coxeter groups.
Book Synopsis Office Hours with a Geometric Group Theorist by : Matt Clay
Download or read book Office Hours with a Geometric Group Theorist written by Matt Clay and published by Princeton University Press. This book was released on 2017-07-11 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric group theory is the study of the interplay between groups and the spaces they act on, and has its roots in the works of Henri Poincaré, Felix Klein, J.H.C. Whitehead, and Max Dehn. Office Hours with a Geometric Group Theorist brings together leading experts who provide one-on-one instruction on key topics in this exciting and relatively new field of mathematics. It's like having office hours with your most trusted math professors. An essential primer for undergraduates making the leap to graduate work, the book begins with free groups—actions of free groups on trees, algorithmic questions about free groups, the ping-pong lemma, and automorphisms of free groups. It goes on to cover several large-scale geometric invariants of groups, including quasi-isometry groups, Dehn functions, Gromov hyperbolicity, and asymptotic dimension. It also delves into important examples of groups, such as Coxeter groups, Thompson's groups, right-angled Artin groups, lamplighter groups, mapping class groups, and braid groups. The tone is conversational throughout, and the instruction is driven by examples. Accessible to students who have taken a first course in abstract algebra, Office Hours with a Geometric Group Theorist also features numerous exercises and in-depth projects designed to engage readers and provide jumping-off points for research projects.
Download or read book ADEX Theory written by Saul Paul Sirag and published by World Scientific. This book was released on 2016 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book shows how the ADE Coxeter graphs unify at least 20 different types of mathematical structures. These mathematical structures are of great utility in unified field theory, string theory, and other areas of physics."--Provided by publisher.
