Unitary Reflection Groups

Author : Gustav I. Lehrer,Donald E. Taylor
Publisher : Cambridge University Press
Page : 303 pages
File Size : 49,5 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 : Gus Lehrer,Donald Ewen Taylor
Publisher : Unknown
Page : 304 pages
File Size : 50,5 Mb
Release : 2014-05-14
Category : Mathematics
ISBN : 051165118X

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Unitary Reflection Groups by Gus Lehrer,Donald Ewen Taylor Pdf

A complete and clear account of the classification of unitary reflection groups, which arise naturally in many areas of mathematics.

Author : Gus Lehrer,Donald Ewen Taylor
Publisher : Unknown
Page : 375 pages
File Size : 47,6 Mb
Release : 2020
Category : Group theory
ISBN : 756039194X

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Unitary Reflection Groups by Gus Lehrer,Donald Ewen Taylor Pdf

Author : L.C. Grove,C.T. Benson
Publisher : Springer Science & Business Media
Page : 142 pages
File Size : 45,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475718690

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Finite Reflection Groups by L.C. Grove,C.T. Benson Pdf

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.

Author : James E. Humphreys
Publisher : Cambridge University Press
Page : 222 pages
File Size : 49,6 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 : Richard Kane
Publisher : Springer Science & Business Media
Page : 382 pages
File Size : 47,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475735420

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Reflection Groups and Invariant Theory by Richard Kane Pdf

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 : V. M. Buchstaber,Sergeĭ Petrovich Novikov,I. M. Krichever
Publisher : American Mathematical Soc.
Page : 338 pages
File Size : 50,9 Mb
Release : 2004
Category : Mathematics
ISBN : 0821836137

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Geometry, Topology, and Mathematical Physics by V. M. Buchstaber,Sergeĭ Petrovich Novikov,I. M. Krichever Pdf

The second half of the 20th century and its conclusion : crisis in the physics and mathematics community in Russia and in the West -- Interview with Sergey P. Novikov -- The w-function of the KdV hierarchy -- On the zeta functions of a meromorphic germ in two variables -- On almost duality for Frobenius manifolds -- Finitely presented semigroups in knot theory. Oriented case -- Topological robotics : subspace arrangements and collision free motion planning -- The initial-boundary value problem on the interval for the nonlinear Schrödinger equation. The algebro-geometric approach. I -- On odd Laplace operators. II -- From 2D Toda hierarchy to conformal maps for domains of the Riemann sphere --Integrable chains on algebraic curves -- Fifteen years of KAM for PDE -- Graded filiform Lie algebras and symplectic nilmanifolds --Adiabatic limit in the Seiberg-Witten equations -- Affine Krichever-Novikov algebras, their representations and applications -- Tame integrals of motion and o-minimal structures.

Author : John Cossey,Charles F. Miller,Walter D. Neumann,Michael Shapiro
Publisher : Walter de Gruyter
Page : 349 pages
File Size : 42,9 Mb
Release : 2011-05-02
Category : Mathematics
ISBN : 9783110806861

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Geometric Group Theory Down Under by John Cossey,Charles F. Miller,Walter D. Neumann,Michael Shapiro Pdf

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Author : Bruce Hunt
Publisher : Springer
Page : 347 pages
File Size : 45,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540699972

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The Geometry of some special Arithmetic Quotients by Bruce Hunt Pdf

The book discusses a series of higher-dimensional moduli spaces, of abelian varieties, cubic and K3 surfaces, which have embeddings in projective spaces as very special algebraic varieties. Many of these were known classically, but in the last chapter a new such variety, a quintic fourfold, is introduced and studied. The text will be of interest to all involved in the study of moduli spaces with symmetries, and contains in addition a wealth of material which has been only accessible in very old sources, including a detailed presentation of the solution of the equation of 27th degree for the lines on a cubic surface.

Author : Bruce Normansell Allison,Gerald Howard Cliff,Canadian Mathematical Society
Publisher : American Mathematical Soc.
Page : 400 pages
File Size : 49,5 Mb
Release : 1995
Category : Mathematics
ISBN : 0821803115

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Representations of Groups by Bruce Normansell Allison,Gerald Howard Cliff,Canadian Mathematical Society Pdf

Representations of Groups contains papers presented at the Canadian Mathematical Society Annual Seminar held in June 1994, in Banff, Alberta, Canada.

Author : Peter Orlik,Hiroaki Terao
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 44,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662027721

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Arrangements of Hyperplanes by Peter Orlik,Hiroaki Terao Pdf

An arrangement of hyperplanes is a finite collection of codimension one affine subspaces in a finite dimensional vector space. Arrangements have emerged independently as important objects in various fields of mathematics such as combinatorics, braids, configuration spaces, representation theory, reflection groups, singularity theory, and in computer science and physics. This book is the first comprehensive study of the subject. It treats arrangements with methods from combinatorics, algebra, algebraic geometry, topology, and group actions. It emphasizes general techniques which illuminate the connections among the different aspects of the subject. Its main purpose is to lay the foundations of the theory. Consequently, it is essentially self-contained and proofs are provided. Nevertheless, there are several new results here. In particular, many theorems that were previously known only for central arrangements are proved here for the first time in completegenerality. The text provides the advanced graduate student entry into a vital and active area of research. The working mathematician will findthe book useful as a source of basic results of the theory, open problems, and a comprehensive bibliography of the subject.

Author : Michel Broué
Publisher : Springer
Page : 150 pages
File Size : 40,6 Mb
Release : 2010-01-28
Category : Mathematics
ISBN : 9783642111754

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Introduction to Complex Reflection Groups and Their Braid Groups by Michel Broué Pdf

This book covers basic properties of complex reflection groups, such as characterization, Steinberg theorem, Gutkin-Opdam matrices, Solomon theorem and applications, including the basic findings of Springer theory on eigenspaces.

Author : Dirk Wiersma,C.T.C. Wall,V. Zakalyukin
Publisher : Springer Science & Business Media
Page : 470 pages
File Size : 54,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401008341

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New Developments in Singularity Theory by Dirk Wiersma,C.T.C. Wall,V. Zakalyukin Pdf

Singularities arise naturally in a huge number of different areas of mathematics and science. As a consequence, singularity theory lies at the crossroads of paths that connect many of the most important areas of applications of mathematics with some of its most abstract regions. The main goal in most problems of singularity theory is to understand the dependence of some objects of analysis, geometry, physics, or other science (functions, varieties, mappings, vector or tensor fields, differential equations, models, etc.) on parameters. The articles collected here can be grouped under three headings. (A) Singularities of real maps; (B) Singular complex variables; and (C) Singularities of homomorphic maps.

Author : Vladimir I. Arnold
Publisher : Springer Science & Business Media
Page : 664 pages
File Size : 54,8 Mb
Release : 2004-06-24
Category : Mathematics
ISBN : 3540206140

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Arnold's Problems by Vladimir I. Arnold Pdf

Vladimir Arnold is one of the most outstanding mathematicians of our time Many of these problems are at the front line of current research

Author : Mark J. Logan
Publisher : Unknown
Page : 212 pages
File Size : 52,7 Mb
Release : 1997
Category : Electronic
ISBN : WISC:89063174890

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Homology and Invariants of Reflection Groups and Lie Algebras by Mark J. Logan Pdf