Unitary Reflection Groups
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Unitary Reflection Groups
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Author : Gustav I. Lehrer
language : en
Publisher: Cambridge University Press
Release Date : 2009-08-13
Unitary Reflection Groups written by Gustav I. Lehrer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-13 with Mathematics categories.
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.
Unitary Reflection Groups
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Author : Gus Lehrer
language : en
Publisher:
Release Date : 2014-05-14
Unitary Reflection Groups written by Gus Lehrer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with Mathematics categories.
A complete and clear account of the classification of unitary reflection groups, which arise naturally in many areas of mathematics.
Introduction To Complex Reflection Groups And Their Braid Groups
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Author : Michel Broué
language : en
Publisher: Springer
Release Date : 2010-01-28
Introduction To Complex Reflection Groups And Their Braid Groups written by Michel Broué and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-28 with Mathematics categories.
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.
Unitary Reflection Groups
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Author : Gus Lehrer
language : en
Publisher:
Release Date : 2020
Unitary Reflection Groups written by Gus Lehrer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Group theory categories.
Reflection Groups And Invariant Theory
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Author : Richard Kane
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Reflection Groups And Invariant Theory written by Richard Kane and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Reflection Groups and their invariant theory provide the main themes of this book and the first two parts focus on these topics. The first 13 chapters deal with reflection groups (Coxeter groups and Weyl groups) in Euclidean Space while the next thirteen chapters study the invariant theory of pseudo-reflection groups. The third part of the book studies conjugacy classes of the elements in reflection and pseudo-reflection groups. The book has evolved from various graduate courses given by the author over the past 10 years. It is intended to be a graduate text, accessible to students with a basic background in algebra. Richard Kane is a professor of mathematics at the University of Western Ontario. His research interests are algebra and algebraic topology. Professor Kane is a former President of the Canadian Mathematical Society.
Reflection Subquotients Of Unitary Reflection Groups
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Author : G. I. Lehrer
language : en
Publisher:
Release Date : 1998
Reflection Subquotients Of Unitary Reflection Groups written by G. I. Lehrer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
Reflection Groups And Coxeter Groups
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Author : James E. Humphreys
language : en
Publisher: Cambridge University Press
Release Date : 1992-10
Reflection Groups And Coxeter Groups written by James E. Humphreys and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-10 with Mathematics categories.
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.
Arrangements Of Hyperplanes
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Author : Peter Orlik
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Arrangements Of Hyperplanes written by Peter Orlik and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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.
New Developments In Singularity Theory
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Author : Dirk Wiersma
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
New Developments In Singularity Theory written by Dirk Wiersma and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Homology And Invariants Of Reflection Groups And Lie Algebras
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Author : Mark J. Logan
language : en
Publisher:
Release Date : 1997
Homology And Invariants Of Reflection Groups And Lie Algebras written by Mark J. Logan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.